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Journal articles on the topic 'Application of linear algebra'

Author: Grafiati

Published: 4 June 2021

Last updated: 17 February 2022

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1

Fabregat-Traver, Diego, and Paolo Bientinesi. "Application-tailored linear algebra algorithms." International Journal of High Performance Computing Applications 27, no. 4 (July 18, 2013): 426–39. http://dx.doi.org/10.1177/1094342013494428.

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2

Deng, Ji Xia. "Application of Linear Algebra in Real Life." Applied Mechanics and Materials 556-562 (May 2014): 3392–95. http://dx.doi.org/10.4028/www.scientific.net/amm.556-562.3392.

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Linear algebra is an important basic course in university mathematics, finite dimensional vector space and linear transformation theory mainly on matrix theory, and the combination of matrix. Concept in linear algebra is defined directly by the mathematical symbol, rarely by example to import. How to make students master the abstract and difficult course, first of all is to let the students find the course in our daily life, to stimulate interest in learning.

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3

Lord, Nick, Charles G. Cullen, David C. Lay, Erwin Kleinfeld, and Margaret Kleinfeld. "Linear Algebra with Applications." Mathematical Gazette 82, no. 493 (March 1998): 153. http://dx.doi.org/10.2307/3620192.

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4

鞠, 桂玲. "Teaching Reform of Linear Algebra Based on Application." Creative Education Studies 08, no. 05 (2020): 688–91. http://dx.doi.org/10.12677/ces.2020.85112.

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5

杨, 威. "Application Examples of Linear Algebra Based on MATLAB." Advances in Applied Mathematics 08, no. 03 (2019): 424–29. http://dx.doi.org/10.12677/aam.2019.83048.

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6

Gohberg, Israel, Peter Lancaster, and Leiba Rodman. "A New Book in Linear Algebra: Indefinite Linear Algebra and Applications." Integral Equations and Operator Theory 53, no. 1 (September 2005): 149–51. http://dx.doi.org/10.1007/s00020-005-1356-6.

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7

Hoa, Dinh Trung, Toan Minh Ho, and Hiroyuki Osaka. "The Linear Span of Projections in AH Algebras and for Inclusions ofC*-Algebras." Abstract and Applied Analysis 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/204319.

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In the first part of this paper, we show that an AH algebraA=lim→(Ai,ϕi)has the LP property if and only if every element of the centre ofAibelongs to the closure of the linear span of projections inA. As a consequence, a diagonal AH-algebra has the LP property if it has small eigenvalue variation in the sense of Bratteli and Elliott. The second contribution of this paper is that for an inclusion of unitalC*-algebrasP⊂Awith a finite Watatani index, if a faithful conditional expectationE:A→Phas the Rokhlin property in the sense of Kodaka et al., thenPhas the LP property under the condition thatAhas the LP property. As an application, letAbe a simple unitalC*-algebra with the LP property,αan action of a finite groupGontoAut(A). Ifαhas the Rokhlin property in the sense of Izumi, then the fixed point algebraAGand the crossed product algebraA ⋊α Ghave the LP property. We also point out that there is a symmetry on the CAR algebra such that its fixed point algebra does not have the LP property.

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8

Qiu, Jianjun, and Yuqun Chen. "Free Lie differential Rota–Baxter algebras and Gröbner–Shirshov bases." International Journal of Algebra and Computation 27, no. 08 (December 2017): 1041–60. http://dx.doi.org/10.1142/s0218196717500485.

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Qiu, Jianjun. "Gröbner–Shirshov bases for commutative algebras with multiple operators and free commutative Rota–Baxter algebras." Asian-European Journal of Mathematics 07, no. 02 (June 2014): 1450033. http://dx.doi.org/10.1142/s1793557114500338.

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In this paper, the Composition-Diamond lemma for commutative algebras with multiple operators is established. As applications, the Gröbner–Shirshov bases and linear bases of free commutative Rota–Baxter algebra, free commutative λ-differential algebra and free commutative λ-differential Rota–Baxter algebra are given, respectively. Consequently, these three free algebras are constructed directly by commutative Ω-words.

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10

Gerrish, F., W. Keith Nicholson, and Harvey Gerber. "Elementary Linear Algebra, with Applications." Mathematical Gazette 75, no. 472 (June 1991): 230. http://dx.doi.org/10.2307/3620286.

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11

Orosi, Greg. "The arithmetico-geometric sequence: an application of linear algebra." International Journal of Mathematical Education in Science and Technology 47, no. 5 (November 9, 2015): 766–72. http://dx.doi.org/10.1080/0020739x.2015.1092180.

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12

Howle, Victoria E., Robert C. Kirby, Kevin Long, Brian Brennan, and Kimberly Kennedy. "Playa: High-Performance Programmable Linear Algebra." Scientific Programming 20, no. 3 (2012): 257–73. http://dx.doi.org/10.1155/2012/606215.

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This paper introduces Playa, a high-level user interface layer for composing algorithms for complex multiphysics problems out of objects from other Trilinos packages. Among other features, Playa provides very high-performance overloaded operators implemented through an expression template mechanism. In this paper, we give an overview of the central Playa objects from a user's perspective, show application to a sequence of increasingly complex solver algorithms, provide timing results for Playa's overloaded operators and other functions, and briefly survey some of the implementation issues involved.

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13

Qiu, Jianjun, and Yuqun Chen. "Gröbner–Shirshov bases for Lie Ω-algebras and free Rota–Baxter Lie algebras." Journal of Algebra and Its Applications 16, no. 10 (September 20, 2017): 1750190. http://dx.doi.org/10.1142/s0219498817501900.

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We generalize the Lyndon–Shirshov words to the Lyndon–Shirshov [Formula: see text]-words on a set [Formula: see text] and prove that the set of all the nonassociative Lyndon–Shirshov [Formula: see text]-words forms a linear basis of the free Lie [Formula: see text]-algebra on the set [Formula: see text]. From this, we establish Gröbner–Shirshov bases theory for Lie [Formula: see text]-algebras. As applications, we give Gröbner–Shirshov bases of a free [Formula: see text]-Rota–Baxter Lie algebra, of a free modified [Formula: see text]-Rota–Baxter Lie algebra, and of a free Nijenhuis Lie algebra and, then linear bases of these three algebras are obtained.

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Abdul Rahim, Rini Hafzah, Aslina Baharum, and Hanafi Hijazi. "Evaluation on effectiveness of learning linear algebra using gamification." Indonesian Journal of Electrical Engineering and Computer Science 17, no. 2 (February 1, 2020): 997. http://dx.doi.org/10.11591/ijeecs.v17.i2.pp997-1004.

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This study evaluate effectiveness of learning Linear Algebra using gamification strategy. In this study, gamification with storytelling strategy is used as teaching tools to attract student to learn Linear Algebra. This study using Polytechnic Malaysia syllabus with focus group of Diploma students for semester three (Mechanical Engineering) and semester four (Electrical Engineering) for two topics; Matrix and Numerical Method. They are five methods of calculation simultaneous linear equations which is ‘Inverse’, ‘Cramer's Rule’, ‘Gauss Elimination’, ‘Lower Upper Doolittle’ and ‘Lower Upper Crout’. They are three main phases to develop this gamification; Pedagogy Phase, Design Phase and Evaluation Phase. Mixed methods approach combining quantitative (survey) and qualitative (Electroencephalogram) is used to evaluate students learning process using Linear Algebra gamification application. The findings of the five items surveyed showed that the acceptance of the prototype of the Linear Algebra Gamification Application was very encouraging from a total of 104 students. This is because all 38 questions for the five items earn a median of four and this indicates the majority of students choose “Agree” and “Strongly Agree”. The findings also show the percent “Agree” and “Strongly Agree” for all questions having a high percentage of between 61.5 and 94.2. This shows more than half satisfied and likes to use the Linear Algebra Gamification Application prototype. With the development of the Linear Algebra Gamification Application prototype, it is hoped that the use of learning based can be extended to a variety of subjects as well as topics to make the learning process more interesting and fun as well as helping to motivate students to learn

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15

Liu, Shanshan, Lina Song, and Rong Tang. "Representations and cohomologies of regular Hom-pre-Lie algebras." Journal of Algebra and Its Applications 19, no. 08 (August 8, 2019): 2050149. http://dx.doi.org/10.1142/s0219498820501492.

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In this paper, first we study dual representations and tensor representations of Hom-pre-Lie algebras. Then we develop the cohomology theory of regular Hom-pre-Lie algebras in terms of the cohomology theory of regular Hom-Lie algebras. As applications, we study linear deformations of regular Hom-pre-Lie algebras, which are characterized by the second cohomology groups of regular Hom-pre-Lie algebras with the coefficients in the regular representations. The notion of a Nijenhuis operator on a regular Hom-pre-Lie algebra is introduced which can generate a trivial linear deformation of a regular Hom-pre-Lie algebra. Finally, we introduce the notion of a Hessian structure on a regular Hom-pre-Lie algebra, which is a symmetric nondegenerate 2-cocycle with the coefficient in the trivial representation. We also introduce the notion of an [Formula: see text]-operator on a regular Hom-pre-Lie algebra, by which we give an equivalent characterization of a Hessian structure.

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16

Zhang, Hui. "The Application of Linear Algebra Algorithm in the Production of Linear Matrix Inequalities." Applied Mechanics and Materials 192 (July 2012): 406–11. http://dx.doi.org/10.4028/www.scientific.net/amm.192.406.

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Discusses the theory and symbolic of the algorithm gives another potential application, but also in the system and control. For example, for the question, has made with special structure, but LMI problem data, may cause factorizations LMI more compact. One can even imagine using the algorithm around, looking for the opportunity to LMI automatic eliminate variables, so simplify problem solving, before they get a lot of influence and a potential solutions. We describe theory, the algorithm can be used to factor in the non commuting variable polynomial matrix and application system switches and control problem into a linear matrix inequality.

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17

JESPERS, ERIC, and DAVID RILEY. "NILPOTENT LINEAR SEMIGROUPS." International Journal of Algebra and Computation 16, no. 01 (February 2006): 141–60. http://dx.doi.org/10.1142/s0218196706002913.

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We characterize the structure of linear semigroups satisfying certain global and local nilpotence conditions and deduce various Engel-type results. For example, using a form of Zel'manov's solution of the restricted Burnside problem we are able to show that a finitely generated residually finite group is nilpotent if and only if it satisfies a certain 4-generator property of semigroups we call WMN. Methods of linear semigroups then allow us to prove that a linear semigroup is Mal'cev nilpotent precisely when it satisfies WMN. As an application, we show that a finitely generated associative algebra is nilpotent when viewed as a Lie algebra if and only if its adjoint semigroup is WMN.

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18

Wang, Qi, Yunhe Sheng, Chengming Bai, and Jiefeng Liu. "Nijenhuis operators on pre-Lie algebras." Communications in Contemporary Mathematics 21, no. 07 (October 10, 2019): 1850050. http://dx.doi.org/10.1142/s0219199718500505.

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First we use a new approach to define a graded Lie algebra whose Maurer–Cartan elements characterize pre-Lie algebra structures. Then using this graded Lie bracket, we define the notion of a Nijenhuis operator on a pre-Lie algebra which generates a trivial deformation of this pre-Lie algebra. There are close relationships between [Formula: see text]-operators, Rota–Baxter operators and Nijenhuis operators on a pre-Lie algebra. In particular, a Nijenhuis operator “connects” two [Formula: see text]-operators on a pre-Lie algebra whose any linear combination is still an [Formula: see text]-operator in certain sense and hence compatible [Formula: see text]-dendriform algebras appear naturally as the induced algebraic structures. For the case of the dual representation of the regular representation of a pre-Lie algebra, there is a geometric interpretation by introducing the notion of a pseudo-Hessian–Nijenhuis structure which gives rise to a sequence of pseudo-Hessian and pseudo-Hessian–Nijenhuis structures. Another application of Nijenhuis operators on pre-Lie algebras in geometry is illustrated by introducing the notion of a para-complex structure on a pre-Lie algebra and then studying para-complex quadratic pre-Lie algebras and para-complex pseudo-Hessian pre-Lie algebras in detail. Finally, we give some examples of Nijenhuis operators on pre-Lie algebras.

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19

Li, Hou Guo. "Application of Lie Group Analysis to the Plastic Torsion of Rod with the Saint Venant–Mises Yield Criterion." Advanced Materials Research 461 (February 2012): 265–71. http://dx.doi.org/10.4028/www.scientific.net/amr.461.265.

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Based on Lie group and Lie algebra theory, the basic principles of Lie group analysis of differential equations in mechanics are analyzed, and its validity in theory of plasticity is explained by example. For the plastic torsion of rod with variable cross section that consists in non-linear Saint Venant-Mises yield criterion, the 10-dimensional Lie algebra admitted by the equilibrium equation and yield criterion is completely solved, and invariants and group invariant solutions relative to different sub-algebras are given. At last, physical explanations of each group invariant solution are discussed by some types of transformations.

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20

Kumari, M. Naga Maruthi, Kavya H.U., and Y. N. Bhavsar. "APPLICATIONS OF LINEAR ALGEBRA IN GENETICS." Journal of Harmonized Research in Applied Science 6, no. 4 (December 30, 2018): 236. http://dx.doi.org/10.30876/johr.6.4.2018.236-240.

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21

Rogers, Jack W. "Applications of Linear Algebra in Calculus." American Mathematical Monthly 104, no. 1 (January 1997): 20–26. http://dx.doi.org/10.1080/00029890.1997.11990592.

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22

Mastronardi, Nicola, and Sabine Van Huffel. "Numerical linear algebra and its applications." Numerical Linear Algebra with Applications 12, no. 8 (2005): 683. http://dx.doi.org/10.1002/nla.443.

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23

Rogers, Jack W. "Applications of Linear Algebra in Calculus." American Mathematical Monthly 104, no. 1 (January 1997): 20. http://dx.doi.org/10.2307/2974819.

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24

Casale, Giuliano. "An application of exact linear algebra to capacity planning models." ACM Communications in Computer Algebra 42, no. 4 (February 6, 2009): 202–5. http://dx.doi.org/10.1145/1504341.1504345.

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25

Timoney, Richard M. "AN INTERNAL CHARACTERIZATION OF COMPLETE POSITIVITY FOR ELEMENTARY OPERATORS." Proceedings of the Edinburgh Mathematical Society 45, no. 2 (June 2002): 285–300. http://dx.doi.org/10.1017/s0013091500000687.

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AbstractComplete positivity of ‘atomically extensible’ bounded linear operators between $C^*$-algebras is characterized in terms of positivity of a bilinear form on certain finite-rank operators. In the case of an elementary operator on a $C^*$-algebra, the approach leads us to characterize k-positivity of the operator in terms of positivity of a quadratic form on a subset of the dual space of the algebra and in terms of a certain inequality involving factorial states of finite type I.As an application we characterize those $C^*$-algebras where every k-positive elementary operator on the algebra is completely positive. They are either k-subhomogeneous or k-subhomogeneous by antiliminal. We also give a dual approach to the metric operator space introduced by Arveson.AMS 2000 Mathematics subject classification: Primary 46L05. Secondary 47B47; 47B65

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26

EBRAHIMI-FARD, KURUSCH, and LI GUO. "FREE ROTA–BAXTER ALGEBRAS AND ROOTED TREES." Journal of Algebra and Its Applications 07, no. 02 (April 2008): 167–94. http://dx.doi.org/10.1142/s0219498808002746.

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A Rota–Baxter algebra, also known as a Baxter algebra, is an algebra with a linear operator satisfying a relation, called the Rota–Baxter relation, that generalizes the integration by parts formula. Most of the studies on Rota–Baxter algebras have been for commutative algebras. Two constructions of free commutative Rota–Baxter algebras were obtained by Rota and Cartier in the 1970s and a third one by Keigher and one of the authors in the 1990s in terms of mixable shuffles. Recently, noncommutative Rota–Baxter algebras have appeared both in physics in connection with the work of Connes and Kreimer on renormalization in perturbative quantum field theory, and in mathematics related to the work of Loday and Ronco on dendriform dialgebras and trialgebras. This paper uses rooted trees and forests to give explicit constructions of free noncommutative Rota–Baxter algebras on modules and sets. This highlights the combinatorial nature of Rota–Baxter algebras and facilitates their further study. As an application, we obtain the unitarization of Rota–Baxter algebras.

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Blute, Richard F. "Hopf algebras and linear logic." Mathematical Structures in Computer Science 6, no. 2 (April 1996): 189–212. http://dx.doi.org/10.1017/s0960129500000943.

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It has recently become evident that categories of representations of Hopf algebras provide fundamental examples of monoidal categories. In this expository paper, we examine such categories as models of (multiplicative) linear logic. By varying the Hopf algebra, it is possible to model several variants of linear logic. We present models of the original commutative logic, the noncommutative logic of Lambek and Abrusci, the braided variant due to the author, and the cyclic logic of Yetter. Hopf algebras provide a unifying framework for the analysis of these variants. While these categories are monoidal closed, they lack sufficient structure to model the involutive negation of classical linear logic. We recall work of Lefschetz and Barr in which vector spaces are endowed with an additional topological structure, called linear topology. The resulting category has a large class of reflexive objects, which form a *-autonomous category, and so model the involutive negation. We show that the monoidal closed structure of the category of representations of a Hopf algebra can be extended to this topological category in a natural and simple manner. The models we obtain have the advantage of being nondegenerate in the sense that the two multiplicative connectives, tensor and par, are not equated. It has been recently shown by Barr that this category of topological vector spaces can be viewed as a subcategory of a certain Chu category. In an Appendix, Barr uses this equivalence to analyze the structure of its tensor product.

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Peise, Elmar, and Paolo Bientinesi. "The ELAPS framework: Experimental Linear Algebra Performance Studies." International Journal of High Performance Computing Applications 33, no. 2 (March 28, 2018): 353–65. http://dx.doi.org/10.1177/1094342018763042.

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In scientific computing, optimal use of computing resources comes at the cost of extensive coding, tuning, and benchmarking. While the classic approach of “features first, performance later” is supported by a variety of tools such as Tau, Vampir, and Scalasca, the emerging performance-centric approach, in which both features and performance are primary objectives, is still lacking suitable development tools. For dense linear algebra applications, we fill this gap with the Experimental Linear Algebra Performance Studies (ELAPS) framework, a multi-platform open-source environment for easy, fast, and yet powerful performance experimentation and prototyping. In contrast to many existing tools, ELAPS targets the beginning of the development process, assisting application developers in both algorithmic and optimization decisions. With ELAPS, users construct experiments to investigate how performance and efficiency depend on factors such as caching, algorithmic parameters, problem size, and parallelism. Experiments are designed either through Python scripts or a specialized Graphical User Interface (GUI), and run on a spectrum of architectures, ranging from laptops to accelerators and clusters. The resulting reports provide various metrics and statistics that can be analyzed both numerically and visually. In this article, we introduce ELAPS and illustrate its practical value in guiding critical performance decisions already in early development stages.

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Chu, Moody T. "Linear algebra algorithms as dynamical systems." Acta Numerica 17 (April 25, 2008): 1–86. http://dx.doi.org/10.1017/s0962492906340019.

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Any logical procedure that is used to reason or to infer either deductively or inductively, so as to draw conclusions or make decisions, can be called, in a broad sense, a realization process. A realization process usually assumes the recursive form that one state develops into another state by following a certain specific rule. Such an action is generally formalized as a dynamical system. In mathematics, especially for existence questions, a realization process often appears in the form of an iterative procedure or a differential equation. For years researchers have taken great effort to describe, analyse, and modify realization processes for various applications.The thrust in this exposition is to exploit the notion of dynamical systems as a special realization process for problems arising from the field of linear algebra. Several differential equations whose solutions evolve in submanifolds of matrices are cast in fairly general frameworks, of which special cases have been found to afford unified and fundamental insights into the structure and behaviour of existing discrete methods and, now and then, suggest new and improved numerical methods. In some cases, there are remarkable connections between smooth flows and discrete numerical algorithms. In other cases, the flow approach seems advantageous in tackling very difficult open problems. Various aspects of the recent development and application in this direction are discussed in this paper.

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30

Beasley, LeRoy B., and Debra A. S. Beasley. "Review of Linear algebra and its application, volume 1: A first course and Linear algebra and its application, volume 2: More advanced by D.H. Griffel." Linear Algebra and its Applications 165 (March 1992): 269–71. http://dx.doi.org/10.1016/0024-3795(92)90243-4.

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Martin, William, Sergio Loch, Laurel Cooley, Scott Dexter, and Draga Vidakovic. "Integrating learning theories and application-based modules in teaching linear algebra." Linear Algebra and its Applications 432, no. 8 (April 2010): 2089–99. http://dx.doi.org/10.1016/j.laa.2009.08.030.

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Gerdt, V. P., A. B. Shvachka, and A. Yu Zharkov. "Computer algebra application for classification of integrable non-linear evolution equations." Journal of Symbolic Computation 1, no. 1 (March 1985): 101–7. http://dx.doi.org/10.1016/s0747-7171(85)80031-6.

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Nepomniaschy, V. A., and A. A. Sulimov. "Problem-oriented verification system and its application to linear algebra programs." Theoretical Computer Science 119, no. 1 (October 1993): 173–85. http://dx.doi.org/10.1016/0304-3975(93)90344-s.

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Pankavich, Stephen, and Rebecca Swanson. "Principal Component Analysis: Resources for an Essential Application of Linear Algebra." PRIMUS 25, no. 5 (December 20, 2014): 400–420. http://dx.doi.org/10.1080/10511970.2014.993446.

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Bientinesi, Paolo, Enrique S. Quintana-Ortí, and Robert A. van de Geijn. "Representing linear algebra algorithms in code: the FLAME application program interfaces." ACM Transactions on Mathematical Software 31, no. 1 (March 2005): 27–59. http://dx.doi.org/10.1145/1055531.1055533.

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Ziegel, Eric R., and James E. Gentle. "Numerical Linear Algebra for Applications in Statistics." Technometrics 41, no. 3 (August 1999): 272. http://dx.doi.org/10.2307/1270592.

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37

Caoimh, C. C. O., and D. H. Griffel. "Linear Algebra and Its Applications, Vol. 2." Mathematical Gazette 73, no. 466 (December 1989): 351. http://dx.doi.org/10.2307/3619331.

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Cowles, Mary Kathryn, James E. Gentle, and Kenneth Lange. "Numerical Linear Algebra for Applications in Statistics." Journal of the American Statistical Association 95, no. 450 (June 2000): 675. http://dx.doi.org/10.2307/2669416.

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Caoimh, C. C. O., and D. H. Griffel. "Linear Algebra and Its Applications, Vol. 1." Mathematical Gazette 73, no. 465 (October 1989): 261. http://dx.doi.org/10.2307/3618483.

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Rodríguez Calderón, Wilson, and Myriam Rocío Pallares Muñoz. "Fortran application to solve systems from NLA using compact storage." DYNA 82, no. 192 (August 25, 2015): 249–56. http://dx.doi.org/10.15446/dyna.v82n192.42423.

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Educational software of Numerical Linear Algebra (NLA) friendly was developed, with the last developments in compact storage formats or compressed formats. This software generates the possibility to have own tools, handling for teaching processes in undergraduate, research and advanced formation. Having a tool own computational for the solution of lineal algebra problems generates advantages, since, all the details, hypothesis, restrictions, applications and kindness of the software can be known of first hand, without necessity of requesting expensive support services. The incorporation of storage advanced elements, programming and acceleration of the solution of NLA problems in the software, not allow alone solve academic cases, but also real problems that induce the user to a better understanding of the problems in an efficient and widespread way.

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41

Schrempf, Konrad. "A standard form in (some) free fields: How to construct minimal linear representations." Open Mathematics 18, no. 1 (November 23, 2020): 1365–86. http://dx.doi.org/10.1515/math-2020-0076.

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Abstract We describe a standard form for the elements in the universal field of fractions of free associative algebras (over a commutative field). It is a special version of the normal form provided by Cohn and Reutenauer and enables the use of linear algebra techniques for the construction of minimal linear representations (in standard form) for the sum and the product of two elements (given in a standard form). This completes “minimal” arithmetic in free fields since “minimal” constructions for the inverse are already known. The applications are wide: linear algebra (over the free field), rational identities, computing the left gcd of two non-commutative polynomials, etc.

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Liang, Xinfeng. "Generalized Jordan N-Derivations of Unital Algebras with Idempotents." Journal of Mathematics 2021 (June 9, 2021): 1–5. http://dx.doi.org/10.1155/2021/9997646.

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Let A be a unital algebra with idempotent e over a 2-torsionfree unital commutative ring ℛ and S : A ⟶ A be an arbitrary generalized Jordan n-derivation associated with a Jordan n-derivation J . We show that, under mild conditions, every generalized Jordan n-derivation S : A ⟶ A is of the form S x = λ x + J x in the current work. As an application, we give a description of generalized Jordan derivations for the condition n = 2 on classical examples of unital algebras with idempotents: triangular algebras, matrix algebras, nest algebras, and algebras of all bounded linear operators, which generalize some known results.

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Watson, James O. "America's Pastime." Mathematics Teacher 86, no. 6 (September 1993): 450–51. http://dx.doi.org/10.5951/mt.86.6.0450.

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Sports statistics, especially those from baseball, furnish interesting and motivating problems for algebra students. The following problem was chosen from Fundamentals of College Algebra (Swokowski 1989) and presented to a class of algebra students to give an example of an application of linear equations.

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Magajna, Bojan. "A System of Operator Equations." Canadian Mathematical Bulletin 30, no. 2 (June 1, 1987): 200–209. http://dx.doi.org/10.4153/cmb-1987-029-2.

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AbstractLet be a separable Hilbert space, the algebra of all bounded operators on and Ai, Bi, ∊ , i = 1,. . . , r. It is shown that if no nontrivial linear combination of the operators Ai, is compact, then there exist X, Y ∊ such that X Ai, Y = Bi, for all i. A related (but much milder) result is discussed in other algebras with the unique maximal ideal and an application to elementary operators is given.

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Jabon, David, Gail Nord, Bryce W. Wilson, Penny Colfman, and John Nord. "Activities: Medical Applications of Systems of Linear Equations." Mathematics Teacher 89, no. 5 (May 1996): 398–410. http://dx.doi.org/10.5951/mt.89.5.0398.

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This activity is aimed at enriching the algebra strand by bringing to the classroom a medical application of systems of linear equations. These problems go beyond the traditional interpretation of systems of equations as intersections of lines and planes and furnish a nice mix of algebraic and geometric concepts. The activity is designed for small-group work.

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Bootland, Carl, Wouter Castryck, Alan Szepieniec, and Frederik Vercauteren. "A framework for cryptographic problems from linear algebra." Journal of Mathematical Cryptology 14, no. 1 (July 21, 2020): 202–17. http://dx.doi.org/10.1515/jmc-2019-0032.

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AbstractWe introduce a general framework encompassing the main hard problems emerging in lattice-based cryptography, which naturally includes the recently proposed Mersenne prime cryptosystem, but also problems coming from code-based cryptography. The framework allows to easily instantiate new hard problems and to automatically construct plausibly post-quantum secure primitives from them. As a first basic application, we introduce two new hard problems and the corresponding encryption schemes. Concretely, we study generalisations of hard problems such as SIS, LWE and NTRU to free modules over quotients of ℤ[X] by ideals of the form (f, g), where f is a monic polynomial and g ∈ ℤ[X] is a ciphertext modulus coprime to f. For trivial modules (i.e. of rank one), the case f = Xn + 1 and g = q ∈ ℤ>1 corresponds to ring-LWE, ring-SIS and NTRU, while the choices f = Xn – 1 and g = X – 2 essentially cover the recently proposed Mersenne prime cryptosystems. At the other extreme, when considering modules of large rank and letting deg(f) = 1, one recovers the framework of LWE and SIS.

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Stănescu, Anca. "On Hopf-Galois extensions of linear categories." Analele Universitatii "Ovidius" Constanta - Seria Matematica 20, no. 3 (December 1, 2012): 111–30. http://dx.doi.org/10.2478/v10309-012-0059-7.

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AbstractWe continue the investigation of H-Galois extensions of linear categories, where H is a Hopf algebra. In our main result, the Theorem 2.2, we characterize this class of extensions in the case when H is finite dimensional. As an application, we prove a version of the Duality Theorem for crossed products with invertible cocycle.

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Park, Kyung-Eun, and Sang-Gu Lee. "Flipped Learning teaching model design and application for the University's "Linear Algebra"." Communications of Mathematical Education 30, no. 1 (February 15, 2016): 1–22. http://dx.doi.org/10.7468/jksmee.2016.30.1.1.

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鞠, 桂玲. "The Application of Case Teaching Method in the Teaching of Linear Algebra." Advances in Education 10, no. 06 (2020): 1035–39. http://dx.doi.org/10.12677/ae.2020.106173.

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Chen, Wen-Haw. "FOUR STAGES IN TEACHING LINEAR ALGEBRA: FROM DIAGNOSIS, CONNECTION, DEEPENING TO APPLICATION." Far East Journal of Mathematical Education 15, no. 2 (October 19, 2015): 177–90. http://dx.doi.org/10.17654/fjmenov2015_177_190.

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