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Journal articles on the topic 'Operations on determinants and matrices'

Author: Grafiati

Published: 5 June 2025

Last updated: 2 August 2025

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1

Ambarawati, Mika, and Shandi Pratama. "Pendekatan Pemecahan Masalah Matematika pada Materi Matriks." Prosiding Seminar Nasional IKIP Budi Utomo 1, no. 01 (2020): 484–93. http://dx.doi.org/10.33503/prosiding.v1i01.936.

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The purpose of this research is to describe a mathematical problem-solving approach to the matrix material. This type of research is qualitative research using library research methods. Data collection techniques by identifying from books, articles, journals, papers, and various information related to mathematical problem-solving approaches to the matrix material. The results showed: (1) the students' way of understanding the problem of types of matrices, calculation operations on matrices, determinants, and inverses; (2) the way students make plans for solving problems with the types of matri

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2

Protacio, Judel Villas. "Computation of Matrix Determinants by Cross-Multiplication: A Rethinking of Dodgson’s Condensation and Reduction by Elementary Row Operations Methods." Symmetry 15, no. 7 (2023): 1456. http://dx.doi.org/10.3390/sym15071456.

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We formulate a more straightforward, symmetry-based technique for manually computing the determinant of any n×n matrix by revisiting Dodgson’s condensation method, as well as strategically applying elementary row (column) operations and the definition and properties of determinants. The result yields a more streamlined algorithm that is generalized through formulas and employs a smaller number of operations and succeeding matrices than the existing methods.

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MANOCHA, DINESH, and JOHN F. CANNY. "A NEW APPROACH FOR SURFACE INTERSECTION." International Journal of Computational Geometry & Applications 01, no. 04 (1991): 491–516. http://dx.doi.org/10.1142/s0218195991000311.

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Evaluating the intersection of two rational parametric surfaces is a recurring operation in solid modeling. However, surface intersection is not an easy problem and continues to be an active topic of research. The main reason lies in the fact that any good surface intersection technique has to balance three conflicting goals of accuracy, robustness and efficiency. In this paper, we formulate the problems of curve and surface intersections using algebraic sets in a higher dimensional space. Using results from Elimination theory, we project the algebraic set to a lower dimensional space. The pro

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4

Jakovčević Stor, Nevena, and Ivan Slapničar. "Inverses and Determinants of Arrowhead and Diagonal-Plus-Rank-One Matrices over Associative Algebras." Axioms 13, no. 6 (2024): 409. http://dx.doi.org/10.3390/axioms13060409.

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This article considers arrowhead and diagonal-plus-rank-one matrices in Fn×n where F∈{R,C,H} and where H is a noncommutative algebra of quaternions. We provide unified formulas for fast determinants and inverses for considered matrices. The formulas are unified in the sense that the same formula holds in both commutative and noncommutative associative fields or algebras, with noncommutative examples being matrices of quaternions and block matrices. Each formula requires O(n) arithmetic operations, as does multiplication of such matrices with a vector. The formulas are efficiently implemented u

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5

Guritman, Sugi, Jaharuddin, Teduh Wulandari Mas'oed, and Siswandi. "A FAST COMPUTATION FOR EIGENVALUES OF CIRCULANT MATRICES WITH ARITHMETIC SEQUENCE." MILANG Journal of Mathematics and Its Applications 19, no. 1 (2023): 69–80. http://dx.doi.org/10.29244/milang.19.1.69-80.

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In this article, we derive simple formulations of the eigenvalues, determinants, and also the inverse of circulant matrices whose entries in the first row form an arithmetic sequence. The formulation of the determinant and inverse is based on elementary row and column operations transforming the matrix to an equivalent diagonal matrix so that the formulation is obtained easily. Meanwhile, for the eigenvalues formulation, we simplify the known result of formulation for the general circulant matrices by exploiting the properties of the cyclic group induced by the set of all roots of as the set o

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6

CULVER, TIM, JOHN KEYSER, DINESH MANOCHA, and SHANKAR KRISHNAN. "A HYBRID APPROACH FOR DETERMINANT SIGNS OF MODERATE-SIZED MATRICES." International Journal of Computational Geometry & Applications 13, no. 05 (2003): 399–417. http://dx.doi.org/10.1142/s0218195903001256.

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Many geometric computations have at their core the evaluation of the sign of the determinant of a matrix. A fast, failsafe determinant sign operation is often a key part of a robust implementation. While linear problems from 3D computational geometry usually require determinants no larger than six, non-linear problems involving algebraic curves and surfaces produce larger matrices. Furthermore, the matrix entries often exceed machine precision, while existing approaches focus on machine-precision matrices. In this paper, we describe a practical hybrid method for computing the sign of the deter

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7

Serbenyuk, Symon. "Matrix analysis: method simplifications." Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia 15 (December 30, 2023): 15–24. http://dx.doi.org/10.24917/20809751.15.2.

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This paper is devoted to explanations of calculation techniques in matrix theory under its teaching and learning, focusing on the notion of matrices and algebraic operations on matrices. Some attention is given to recommendations for teaching of determinants. A purpose of the main part of the article is to provide recommendations for lecturers to help them in teaching matrix theory, in a way that will enable for students to understand the content studied in a short time. Auxiliary schemes, short notations, and recommendations are given.

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8

Jung, Dong-Won, U.-Rae Kim, Jungil Lee, and Chaehyun Yu. "Lagrange-multiplier regularization of eigenproblem for Jx." Journal of the Korean Physical Society 79, no. 12 (2021): 1089–103. http://dx.doi.org/10.1007/s40042-021-00316-7.

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AbstractWe solve the eigenproblem of the angular momentum $$J_x$$ J x by directly dealing with the non-diagonal matrix unlike the conventional approach rotating the trivial eigenstates of $$J_z$$ J z . Characteristic matrix is reduced into a tri-diagonal form following Narducci–Orszag rescaling of the eigenvectors. A systematic reduction formalism with recurrence relations for determinants of any dimension greatly simplifies the computation of tri-diagonal matrices. Thus the secular determinant is intrinsically factorized to find the eigenvalues immediately. The reduction formalism is employed

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9

Anuja, Kisanrao Raundal. "A Study on the Linear Algebra." International Journal of Innovative Science and Research Technology 7, no. 10 (2022): 1923–26. https://doi.org/10.5281/zenodo.7338672.

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Linear algebra is an initial part of mathematics. It is a major branch of arithmetic related to the mathematical systems underlying the operations of addition and scalar multiplication, consisting of the principles of construction of linear equations, matrices, determinants, vector surfaces, and linear transformations. Linear algebra is a mathematical subject that deals with vectors and matrices, and more generally with vector surfaces and linear transformations. Unlike the other components of arithmetic, which are often fueled by new ideas and unsolved problems, linear algebra is very easy to

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10

Alfahal, Abuobida M. A., Barbara .., Raja Abdullah Abdulfatah, Yaser Ahmad Alhasan, and Husain Alhayek. "An Approach To Symbolic n-Plithogenic Square Real Matrices For 9≤ n ≤12." International Journal of Neutrosophic Science 22, no. 2 (2023): 35–53. http://dx.doi.org/10.54216/ijns.220204.

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The concept of symbolic n-plithogenic algebraic matrices as symmetric structures with n+1 symmetric classical components with the special definition of the multiplication operation. This paper is dedicated to studying the properties of symbolic 10, and 9-plithogenic real square matrices and 11, 12-plithogenic real matrices from algebraic point of view, where algorithms for computing the eigenvalues and determinants will be proved. Also, the inverse of a symbolic n-plithogenic matrix for the special values n=10, n=9, n=11, and n=12 will be presented.

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11

Wang, Heng, and Changheng Zhao. "Some explorations of linear algebra." Highlights in Science, Engineering and Technology 49 (May 21, 2023): 563–70. http://dx.doi.org/10.54097/hset.v49i.8614.

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It is a fundamental problem in quantum information whether a particular quantum state of a composite system is entangled. It has enormous potential in quantum error correction, quantum cryptography, and quantum teleportation applications. This problem can be transferred in the form of a mathematical conjecture in language of linear algebra. In this paper, the authors explain the important applications, convenience, efficiency of using linear algebra in math physics, and computer science. The authors give some examples of linear algebra used in various areas, including datum coordinate system f

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12

Valvi, F. N. "A Generalization of a Class of Matrices: Analytic Inverse and Determinant." Advances in Numerical Analysis 2011 (December 1, 2011): 1–6. http://dx.doi.org/10.1155/2011/593548.

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The aim of this paper is to present the structure of a class of matrices that enables explicit inverse to be obtained. Starting from an already known class of matrices, we construct a Hadamard product that derives the class under consideration. The latter are defined by parameters, analytic expressions of which provide the elements of the lower Hessenberg form inverse. Recursion formulae of these expressions reduce the arithmetic operations in evaluating the inverse to .

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13

Jvana Wahyu Pratami, Nabila Nabila, and Rina Sunaryani. "Analisis Pemahaman Konsep Perkalian Matriks Dalam Pembelajaran Matematika Kelas 11." Konstanta : Jurnal Matematika dan Ilmu Pengetahuan Alam 1, no. 3 (2023): 65–71. https://doi.org/10.59581/konstanta.v1i3.944.

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The research was conducted to determine students' ability to solve problems with matrix material. This study used descriptive qualitative research and took 20 class XI students of SMK Bina Bangsa as research objects. The techniques used to collect research data are 3 instruments in the form of question descriptions and questionnaire forms. Data analysis in this study used data reduction, data presentation, and drawing conclusions. As a result of this study, students of class XI at SMK Bina Bangsa did not do well in mastering the matrix material and understanding the concepts. The reason studen

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14

Guritman, Sugi, Jaharuddin, Teduh Wulandari, and Siswandi. "An Efficient Method for Computing the Inverse and Eigenvalues of Circulant Matrices with Lucas Numbers." Journal of Advances in Mathematics and Computer Science 39, no. 4 (2024): 10–23. http://dx.doi.org/10.9734/jamcs/2024/v39i41879.

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In this article, the inverse including the determinant, and the eigenvalues of circulant matrices with entry Lucas numbers are formulated explicitly in a simple way so that their computations can be constructed efficiently. The formulation method of the determinant and inverse is simply applying the theory of elementary row or column operations and can be unified in one theorem. Meanwhile, for the eigenvalues formulation, the recently known formulation in the case of general circulant matrices is simplified by observing the specialty of the Lucas sequence and applying cyclic group properties o

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15

Charlier, Christophe, and Tom Claeys. "Thinning and conditioning of the circular unitary ensemble." Random Matrices: Theory and Applications 06, no. 02 (2017): 1750007. http://dx.doi.org/10.1142/s2010326317500071.

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We apply the operation of random independent thinning on the eigenvalues of [Formula: see text] Haar distributed unitary random matrices. We study gap probabilities for the thinned eigenvalues, and we study the statistics of the eigenvalues of random unitary matrices which are conditioned such that there are no thinned eigenvalues on a given arc of the unit circle. Various probabilistic quantities can be expressed in terms of Toeplitz determinants and orthogonal polynomials on the unit circle, and we use these expressions to obtain asymptotics as [Formula: see text].

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16

K., Appukuttan K., and Suma Bhat. "An Alternate Method for Computation of Transfer Function Matrix." Journal of Control Science and Engineering 2010 (2010): 1–3. http://dx.doi.org/10.1155/2010/789404.

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A direct and simple numerical method is presented for calculating the transfer function matrix of a linear time invariant multivariable system (A,B,C). The method is based on the matrix-determinant identity, and it involves operations with an auxiliary vector on the matrices. The method is computationally faster compared to Liverrier and Danilevsky methods.

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17

SEYDEL, R. "ON DETECTING STATIONARY BIFURCATIONS." International Journal of Bifurcation and Chaos 01, no. 02 (1991): 335–37. http://dx.doi.org/10.1142/s0218127491000257.

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Locating stationary bifurcations amounts to measuring the singularity of parameter-dependent Jacobian matrices. A well-known example of a measure of singularity is the determinant, requiring O(n) operations to calculate when a decomposition of the matrix is available. This paper discusses an alternative for the case of rank-deficiency one. An algorithm will be based on elements of the inverse Jacobian. The alternative has useful scaling properties, providing estimates of a sensitivity analysis.

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18

SISWANDI, SISWANDI, SUGI GURITMAN, NUR ALIATININGTYAS, and TEDUH WULANDARI. "A COMPUTATION PERSPECTIVE FOR THE EIGENVALUES OF CIRCULANT MATRICES INVOLVING GEOMETRIC PROGRESSION." Jurnal Matematika UNAND 12, no. 1 (2023): 65. http://dx.doi.org/10.25077/jmua.12.1.65-77.2023.

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In this article, the eigenvalues and inverse of circulant matrices with entries in the first row having the form of a geometric sequence are formulated explicitly in a simple form in one theorem. The method for deriving the formulation of the determinant and inverse is simply using elementary row or column operations. For the eigenvalues, the known formulation of the previous results is simplified by considering the specialty of the sequence and using cyclic group properties of unit circles in the complex plane. Then, the algorithm of eigenvalues formulation is constructed, and it shows as a b

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19

Jannah, Miftahul, and Yusmet Rizal. "Matriks Toeplitz dan Determinannya Menggunakan Metode Salihu." Journal of Mathematics UNP 8, no. 2 (2023): 8. http://dx.doi.org/10.24036/unpjomath.v8i2.14240.

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The matrix is a rectangular array of numbers. In this range the numbers are called the entries of the matrix. In matrix calculations generally focus on square-shaped matrices. There is a matrix called the Toeplitz matrix. The Toeplitz matrix has the same operations and calculations as a square matrix in general, one method for calculating the determinant is the Sarrus method. There is an alternative method to solve the determinant of the matrix, namely the Salihu determinant. The purpose of this research is to know the determinant properties related to the Toeplitz matrix and to know the deter

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20

Ariyanti, Gregoria. "A NOTE ON THE SOLUTION OF THE CHARACTERISTIC EQUATION OVER THE SYMMETRIZED MAX-PLUS ALGEBRA." BAREKENG: Jurnal Ilmu Matematika dan Terapan 16, no. 4 (2022): 1347–54. http://dx.doi.org/10.30598/barekengvol16iss4pp1347-1354.

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The symmetrized max-plus algebra is an extension of max-plus algebra. One of the problems in the symmetrized max-plus algebra is determining the eigenvalues of a matrix. If the determinant can be defined, the characteristic equation can be formulated as a max-plus algebraic multivariate polynomial equation system. A mathematical tool for solving the problem using operations as in conventional algebra, known as the extended linear complementary problem (ELCP), to determine the solution to the characteristic equation. In this paper, we will describe the use of ELCP in determining the solution to

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21

Stepanenko, D. A., and A. N. Kindruk. "Variational Problem on Vibrations of Unequal-Thickness Rings and Its Application for Calculating Ultrasonic Vibration Concentrators." Science & Technique 23, no. 4 (2024): 295–303. http://dx.doi.org/10.21122/2227-1031-2024-23-4-295-303.

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The paper considers a method for calculating the natural frequencies of vibrations of unequal-thickness rings, based on application of Hamilton’s variational principle and theories of vibrations of curved beams of the Euler-Bernoulli and Timoshenko type. Solutions of the problem are represented as Fourier series providing possibility of its reduction to the system of linear algebraic equations. The problem of determining natural frequencies is reduced to a generalized problem for the eigenvalues of matrices. Based on a comparison of the numerical results obtained for an eccentric ring with the

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22

Julian, Maureen. "Color-Coding Point Group & Space Group Diagrams and other Mathematical Journeys." Acta Crystallographica Section A Foundations and Advances 70, a1 (2014): C1275. http://dx.doi.org/10.1107/s2053273314087245.

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Color clarifies diagrams point group and space group diagrams. For example, consider the general position diagrams and the symbol diagrams. Symmetry operations can be represented by matrices whose determinant is either plus one or minus one. In the former case there is no change of handedness and in the latter case there is a change of handedness. The general position diagrams emphasis this information by color-coding. The symbol diagrams are a little more complicated and will be demonstrated. The second topic is a comparison of the thirty-two three-dimensional point groups with their correspo

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23

Jeng, Shyr-Long, Rohit Roy, and Wei-Hua Chieng. "A Matrix Approach for Analyzing Signal Flow Graph." Information 11, no. 12 (2020): 562. http://dx.doi.org/10.3390/info11120562.

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Mason’s gain formula can grow factorially because of growth in the enumeration of paths in a directed graph. Each of the (n − 2)! permutation of the intermediate vertices includes a path between input and output nodes. This paper presents a novel method for analyzing the loop gain of a signal flow graph based on the transform matrix approach. This approach only requires matrix determinant operations to determine the transfer function with complexity O(n3) in the worst case, therefore rendering it more efficient than Mason’s gain formula. We derive the transfer function of the signal flow graph

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NIKITIN, Yu R., and S. A. TREFILOV. "DEVELOPMENT OF DIAGNOSTIC SYSTEM FOR MOBILE ROBOT DRIVES." Fundamental and Applied Problems of Engineering and Technology 4, no. 1 (2020): 59–67. http://dx.doi.org/10.33979/2073-7408-2020-342-4-1-59-67.

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This paper presents the results of a study of the influence of the technical condition of mobile robot drives on the identifiability criterion. A discrete robot model has been developed with optimal drive control. The results of computational experiments are presented, confirming the hypothesis of a nonlinear dependence of the determinants of the expanded state matrix and measurements in the robot model, significantly affecting its control. The identification criterion of the robot as a determinant of an expanded state matrix consisting of a combination of a state matrix and a measurement matr

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Ibrahimov, F., N. Jabrayilova, and Kh. Ilyasov. "INTERPRETATION OF THE PROCESS OF MASTERING "THEORETICAL AND TECHNOLOGICAL BASES OF SOLVING THE SYSTEM OF LINEAR ALGEBRAIC EQUATIONS" IN THE TEACHING OF "ALGEBRA"." Sciences of Europe, no. 112 (May 8, 2023): 60–66. https://doi.org/10.5281/zenodo.7907324.

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In the article, it is emphasized that systems with an arbitrary number of equations and an arbitrary number of unknowns are studied in “Algebra”, which has a special place among the compulsory subjects of the “Mathematics teaching” specialty in pedagogically oriented higher schools, and attention is directed to the possible forms of the System of Linear Algebraic Equations (SLAE). The concepts of “equivalence” and “elementary transformation” are explained by noting the important role of the concept of equivalence and equivalence of the system of

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Atanassov, Krassimir T., Peter Vassilev, Vassia Atanassova, et al. "Generalized Net Model of Forest Zone Monitoring by UAVs." Mathematics 9, no. 22 (2021): 2874. http://dx.doi.org/10.3390/math9222874.

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The paper presents a generalized net (GN) model of the process of terrain observation with the help of unmanned aerial vehicles (UAVs) for the prevention and rapid detection of wildfires. Using a GN, the process of monitoring a zone (through a UAV, which is further called a reconnaissance drone) and the localization of forest fires is described. For a more indepth study of the terrain, the reconnaissance drone needs to coordinate with a second UAV, called a specialized drone, so that video and sensory information is provided to the supervising fire command operational center. The proposed GN m

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27

Stróż, Kazimierz. "Symmetry of semi-reduced lattices." Acta Crystallographica Section A Foundations and Advances 71, no. 3 (2015): 268–78. http://dx.doi.org/10.1107/s2053273315001096.

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The main result of this work is extension of the famous characterization of Bravais lattices according to their metrical, algebraic and geometric properties onto a wide class of primitive lattices (including Buerger-reduced, nearly Buerger-reduced and a substantial part of Delaunay-reduced) related to low-restrictedsemi-reduced descriptions(s.r.d.'s). While the `geometric' operations in Bravais lattices map the basis vectors into themselves, the `arithmetic' operators in s.r.d. transform the basis vectors into cell vectors (basis vectors, face or space diagonals) and are represented by matrice

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Jeni Seles Martina, D., and G. Deepa. "Some algebraic properties on rough neutrosophic matrix and its application to multi-criteria decision-making." AIMS Mathematics 8, no. 10 (2023): 24132–52. http://dx.doi.org/10.3934/math.20231230.

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<abstract><p>Rough set theory is a method of information processing for database systems. The neutrosophic matrix is a generalization of the fuzzy matrix, especially in handling indeterminacy situations. The concept of matrix theory and its energy in the neutrosophic environment help to determine the value of the uncertain matrix. In this paper, we correlate the rough set theory with the neutrosophic matrix theory to introduce the rough neutrosophic matrix (RNM). In this structure, lower and upper approximation neutrosophic matrices are used to deal with uncertain situations. We de

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29

Miler, Ryszard K., Marcin J. Kisielewski, Anna Brzozowska, and Antonina Kalinichenko. "Efficiency of Telematics Systems in Management of Operational Activities in Road Transport Enterprises." Energies 13, no. 18 (2020): 4906. http://dx.doi.org/10.3390/en13184906.

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Implemented in road transport enterprises (RTEs) on a large scale, telematics systems are dedicated both to the particular aspects of their operation and to the integrated fields of the total operational functioning of such entities. Hence, a research problem can be defined as the identification of their efficiency levels in the context of operational activities undertaken by RTEs (including more holistic effects, e.g., lowering fuel/energy consumption and negative environmental impacts). Current research studies refer to the efficiency of some particular modules, but there have not been any p

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DERIABINA, Y., and N. KRAVCHENKO. "THE USE OF MAXIMA MOBILE APPLICATION IN THE PROCESS OF TEACHING HIGHER MATHEMATICS." Scientific papers of Berdiansk State Pedagogical University Series Pedagogical sciences 1, no. 1 (2023): 225–35. http://dx.doi.org/10.31494/2412-9208-2023-1-1-225-235.

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Today, the educational process of higher educational institutions of Ukraine is undergoing changes and needs innovations. Recently, due to the transition to distance learning, the introduction of martial law, aerial alarms and unstable Internet connection, teachers and students must learn to quickly adapt to the relevant situations and continue to carry out online educational activities at a high level. With the transition to distance learning, the implementation of mobile learning has become relevant, which involves the use of mobile and portable devices (phones, laptops, tablets) for teachin

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George, Kiernan, and Alan J. Michaels. "Designing a Block Cipher in Galois Extension Fields for IoT Security." IoT 2, no. 4 (2021): 669–87. http://dx.doi.org/10.3390/iot2040034.

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This paper focuses on a block cipher adaptation of the Galois Extension Fields (GEF) combination technique for PRNGs and targets application in the Internet of Things (IoT) space, an area where the combination technique was concluded as a quality stream cipher. Electronic Codebook (ECB) and Cipher Feedback (CFB) variations of the cryptographic algorithm are discussed. Both modes offer computationally efficient, scalable cryptographic algorithms for use over a simple combination technique like XOR. The cryptographic algorithm relies on the use of quality PRNGs, but adds an additional layer of s

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32

Zubov, N. E., and V. N. Ryabchenko. "Solution of a Linear Nondegenerate Matrix Equation Based on the Zero Divisor." Herald of the Bauman Moscow State Technical University. Series Natural Sciences, no. 5 (98) (October 2021): 49–59. http://dx.doi.org/10.18698/1812-3368-2021-5-49-59.

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New formulas were obtained to solve the linear non-degenerate matrix equations based on zero divisors of numerical matrices. Two theorems were formulated, and a proof to one of them is provided. It is noted that the proof of the second theorem is similar to the proof of the first one. The proved theorem substantiates new formula in solving the equation equivalent in the sense of the solution uniqueness to the known formulas. Its fundamental difference lies in the following: any explicit matrix inversion or determinant calculation is missing; solution is "based" not on the left, but on the righ

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33

Litvinenko, Alexander, David Keyes, Venera Khoromskaia, Boris N. Khoromskij, and Hermann G. Matthies. "Tucker Tensor Analysis of Matérn Functions in Spatial Statistics." Computational Methods in Applied Mathematics 19, no. 1 (2019): 101–22. http://dx.doi.org/10.1515/cmam-2018-0022.

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AbstractIn this work, we describe advanced numerical tools for working with multivariate functions and for the analysis of large data sets. These tools will drastically reduce the required computing time and the storage cost, and, therefore, will allow us to consider much larger data sets or finer meshes. Covariance matrices are crucial in spatio-temporal statistical tasks, but are often very expensive to compute and store, especially in three dimensions. Therefore, we approximate covariance functions by cheap surrogates in a low-rank tensor format. We apply the Tucker and canonical tensor dec

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Lapin, A. V., N. E. Zubov, and A. V. Proletarskii. "Generalization of Ackermann Formula for a Certain Class of Multidimensional Dynamic Systems with Vector Input." Herald of the Bauman Moscow State Technical University. Series Natural Sciences, no. 4 (109) (August 2023): 18–38. http://dx.doi.org/10.18698/1812-3368-2023-4-18-38.

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A compact analytical formula is obtained that determines the entire set of solutions of the modal control problem for a wide class of multidimensional dynamical systems with vector input, where the number of states is divisible by the number of control inputs, and the controllability index is equal to the quotient of this division. This formula generalizes to systems with the vector input the Ackermann formula applied to multidimensional systems with scalar input. The basis to obtaining the generalized Ackermann formula lies in the original concepts of the Luenberger generalized canonical form

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35

Jasim, Niran sabah, Mohammed Ibrahem Lfta, and Ahmad Issa. "Score for the Group SL(2,38)." Ibn AL-Haitham Journal For Pure and Applied Sciences 36, no. 3 (2023): 408–15. http://dx.doi.org/10.30526/36.3.3017.

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The set of all (n×n) non-singular matrices over the field F. And this set forms a group under the operation of matrix multiplication. This group is called the general linear group of dimension over the field F, denoted by . The determinant of these matrices is a homomorphism from into F* and the kernel of this homomorphism was the special linear group and denoted by Thus is the subgroup of which contains all matrices of determinant one. The rationally valued characters of the rational representations are written as a linear combination of the induced characters for the groups discussed in this

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S, Niran Sabah Jasim, Mohammed Salah Aldeen Zidan, Azza I.M.S. Abu-Shams, and Ahmad Issa. "Outcome for the group SL(2,57)." Ibn AL-Haitham Journal For Pure and Applied Sciences 37, no. 1 (2024): 403–11. http://dx.doi.org/10.30526/37.1.3018.

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The set of all (n×n) non-singular matrices over the field F this set forms a group under the operation of matrix multiplication. This group is called the general linear group of dimension over the field F, denoted by . The determinant of these matrices is a homomorphism from into F* and the kernel of this homomorphism was the special linear group and denoted by Thus is the subgroup of which contains all matrices of determinant one. The rational valued characters of the rational representations written as a linear combination of the induced characters for the groups discuss in this paper and fi

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Silvester, John R. "Determinants of Block Matrices." Mathematical Gazette 84, no. 501 (2000): 460. http://dx.doi.org/10.2307/3620776.

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Maybee, John S., D. D. Olesky, Driessche P. van den, and G. Wiener. "Matrices, Digraphs, and Determinants." SIAM Journal on Matrix Analysis and Applications 10, no. 4 (1989): 500–519. http://dx.doi.org/10.1137/0610036.

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Horáček, Jaroslav, Milan Hladík, and Josef Matějka. "Determinants of Interval Matrices." Electronic Journal of Linear Algebra 33 (May 16, 2018): 99–112. http://dx.doi.org/10.13001/1081-3810.3719.

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In this paper we shed more light on determinants of real interval matrices. Computing the exact bounds on a determinant of an interval matrix is an NP-hard problem. Therefore, attention is first paid to approximations. NP-hardness of both relative and absolute approximation is proved. Next, methods computing verified enclosures of interval determinants and their possible combination with preconditioning are discussed. A new method based on Cramer's rule was designed. It returns similar results to the state-of-the-art method, however, it is less consuming regarding computational time. Other met

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Basor, Estelle L., Yang Chen, and Harold Widom. "Determinants of Hankel Matrices." Journal of Functional Analysis 179, no. 1 (2001): 214–34. http://dx.doi.org/10.1006/jfan.2000.3672.

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Reinhart, Georg Martin. "Determinants of Partition Matrices." Journal of Number Theory 56, no. 2 (1996): 283–97. http://dx.doi.org/10.1006/jnth.1996.0018.

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Hossne, García Américo. "Arithmetic matrix calculation in visual basic." SABER 34 (May 20, 2022): 62–87. https://doi.org/10.5281/zenodo.7957878.

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<strong>Abstract</strong> Arithmetic matrix calculation for multiplication of two or more arrays, determinant, inversion, division, addition, subtraction and transposition are common in algebra applications. The program procedures uses grids and list table of change able sizes to prompt better responses according to matrix sizes, obeying automatically with arithmetic rules. The objective consisted in presenting a program using Visual Basic method accomplishing the algebraic procedures. The package resulted flexible, practical and adaptable. As a result due to counting the number of processes (

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Moghaddamfar, A. R. "DETERMINANTS OF SEVERAL MATRICES ASSOCIATED WITH PASCAL'S TRIANGLE." Asian-European Journal of Mathematics 03, no. 01 (2010): 119–31. http://dx.doi.org/10.1142/s1793557110000088.

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Pascal's triangle is one of the most well-known arithmetical triangles and has many wonderful properties. This triangle may be rearranged so that one can consider various matrices. When these matrices are squares, we can discuss their determinants. Our purpose of this article is to study the determinants of square matrices related to Pascal's triangle where the determinants are equal to an entry in a particular place. We also consider the square matrices whose determinants are related to their dimensions only.

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Kovacs, Istvan, Daniel S. Silver, and Susan G. Williams. "Determinants of Commuting-Block Matrices." American Mathematical Monthly 106, no. 10 (1999): 950. http://dx.doi.org/10.2307/2589750.

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Chapman, Robin. "Determinants of Legendre symbol matrices." Acta Arithmetica 115, no. 3 (2004): 231–44. http://dx.doi.org/10.4064/aa115-3-4.

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Hilberdink, Titus. "Determinants of multiplicative Toeplitz matrices." Acta Arithmetica 125, no. 3 (2006): 265–84. http://dx.doi.org/10.4064/aa125-3-4.

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Losonczi, László. "Determinants of some pentadiagonal matrices." Glasnik Matematicki 56, no. 2 (2021): 271–86. http://dx.doi.org/10.3336/gm.56.2.05.

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In this paper we consider pentadiagonal \((n+1)\times(n+1)\) matrices with two subdiagonals and two superdiagonals at distances \(k\) and \(2k\) from the main diagonal where \(1\le k \lt 2k\le n\). We give an explicit formula for their determinants and also consider the Toeplitz and “imperfect” Toeplitz versions of such matrices. Imperfectness means that the first and last \(k\) elements of the main diagonal differ from the elements in the middle. Using the rearrangement due to Egerváry and Szász we also show how these determinants can be factorized.

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Bruhn, Henning, and Dieter Rautenbach. "Maximal determinants of combinatorial matrices." Linear Algebra and its Applications 553 (September 2018): 37–57. http://dx.doi.org/10.1016/j.laa.2018.04.030.

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Gil', Michael. "Perturbations of determinants of matrices." Linear Algebra and its Applications 590 (April 2020): 235–42. http://dx.doi.org/10.1016/j.laa.2019.12.044.

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Stuart, Jeffrey L. "Determinants of Hessenberg L-Matrices." SIAM Journal on Matrix Analysis and Applications 12, no. 1 (1991): 7–15. http://dx.doi.org/10.1137/0612002.

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