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Journal articles on the topic 'Moore penrose'

Author: Grafiati

Published: 7 June 2025

Last updated: 2 August 2025

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1

Mardiyana, Mardiyana, Na'imah Hijriati, and Thresye Thresye. "INVERS TERGENERALISASI MOORE PENROSE." EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN 15, no. 2 (2022): 78. http://dx.doi.org/10.20527/epsilon.v15i2.3667.

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The generalized inverse is a concept for determining the inverse of a singular matrix and and matrix which has the characteristic of the inverse matrix. There are several types of generalized inverse, one of which is the Moore-Penrose inverse. The matrix is called Moore Penrose inverse of a matrix if it satisfies the four penrose equations and is denoted by . Furthermore, if the matrix satisfies only the first two equations of the Moore-Penrose inverse and , then is called the group inverse of and is denoted by . The purpose of this research was to determine the group inverse of a non-diagonal

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2

Chen, Yang, Kezheng Zuo, and Zhimei Fu. "New characterizations of the generalized Moore-Penrose inverse of matrices." AIMS Mathematics 7, no. 3 (2022): 4359–75. http://dx.doi.org/10.3934/math.2022242.

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<abstract><p>Some new characterizations of the generalized Moore-Penrose inverse are proposed using range, null space, several matrix equations and projectors. Several representations of the generalized Moore-Penrose inverse are given. The relationships between the generalized Moore-Penrose inverse and other generalized inverses are discussed using core-EP decomposition. The generalized Moore-Penrose matrices are introduced and characterized. One relation between the generalized Moore-Penrose inverse and corresponding nonsingular border matrix is presented. In addition, application

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3

Zuo, Kezheng, Yang Chen, and Li Yuan. "Further representations and computations of the generalized Moore-Penrose inverse." AIMS Mathematics 8, no. 10 (2023): 23442–58. http://dx.doi.org/10.3934/math.20231191.

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<abstract><p>The aim of this paper is to provide new representations and computations of the generalized Moore-Penrose inverse. Based on the Moore-Penrose inverse, group inverse, Bott-Duffin inverse and certain projections, some representations for the generalized Moore-Penrose inverse are given. An equivalent condition for the continuity of the generalized Moore-Penrose inverse is proposed. Splitting methods and successive matrix squaring algorithm for computing the generalized Moore-Penrose inverse are presented.</p></abstract>

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4

Morillas, Patricia. "Expressions and characterizations for the Moore-Penrose inverse of operators and matrices." Electronic Journal of Linear Algebra 39 (May 18, 2023): 214–41. http://dx.doi.org/10.13001/ela.2023.7315.

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Under certain conditions, we prove that the Moore-Penrose inverse of a sum of operators is the sum of the Moore-Penrose inverses. From this, we derive expressions and characterizations for the Moore-Penrose inverse of an operator that are useful for its computation. We give formulations of them for finite matrices and study the Moore-Penrose inverse of circulant matrices and of distance matrices of certain graphs.

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5

Xiao, Qi, and Jin Zhong. "Characterizations and properties of hyper-dual Moore-Penrose generalized inverse." AIMS Mathematics 9, no. 12 (2024): 35125–50. https://doi.org/10.3934/math.20241670.

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<p>In this paper, the definition of the hyper-dual Moore-Penrose generalized inverse of a hyper-dual matrix is introduced. Characterizations for the existence of the hyper-dual Moore-Penrose generalized inverse are given, and a formula for the hyper-dual Moore-Penrose generalized inverse is presented whenever it exists. Least-squares properties of the hyper-dual Moore-Penrose generalized inverse are discussed by introducing a total order of hyper-dual numbers. We also introduce the definition of a dual matrix of order $ n $. A necessary and sufficient condition for the existence of the M

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6

Ani, Ani, Mashadi Mashadi, and Sri Gemawati. "Invers Moore-Penrose pada Matriks Turiyam Simbolik Real." Jambura Journal of Mathematics 5, no. 1 (2023): 95–114. http://dx.doi.org/10.34312/jjom.v5i1.16304.

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The symbolic Turiyam matrix is a matrix whose entries contain symbolic Turiyam. Inverse matrices can generally be determined if the matrix is a non-singular square matrix. Currently the inverse of the symbolic Turiyam matrix of size m × n with m 6= n can be determined by the Moore-Penrose inverse. The purpose of this research is to determine the inverse Moore-Penrose algorithm on a real symbolic Turiyam matrix of size m × n with m 6= n. Algebraic operations on symbolic Turiyam is a method used to obtain the Moore-Penrose inverse on real symbolic Turiyam matrices by applying symbolic Turiyam al

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7

ÁNH, PHAM NGOC, and LÁSZLÓ MÁRKI. "MOORE–PENROSE LOCALIZATION." Journal of Algebra and Its Applications 03, no. 01 (2004): 1–8. http://dx.doi.org/10.1142/s0219498804000666.

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For rings with involution, we describe the close interrelation between localizations with respect to group inverses and Moore–Penrose inverses, respectively. In full generality, we show that Moore–Penrose localizations are equivalent with certain Fountain–Gould localizations, and that "full" Moore–Penrose and Fountain–Gould orders, respectively, coincide in a perfect or strongly regular ring.

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8

Misic, Milan, Marina Tosic, and Zoran Popovic. "Generalized inverses of a linear combination of Moore-Penrose hermitian matrices." Filomat 30, no. 11 (2016): 2965–72. http://dx.doi.org/10.2298/fil1611965m.

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In this paper we give a representation of the Moore-Penrose inverse and the group inverse of a linear combination of Moore-Penrose Hermitian matrices, i.e., square matrices satisfying Ay = A. Also, we consider the invertibility of some linear combination of commuting Moore-Penrose Hermitian matrices.

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9

Zakiya, Annisa Maula, Yanita ., and Nova Noliza Bakar. "MENENTUKAN INVERS MOORE-PENROSE DENGAN METODE BEN NOBLE." Jurnal Matematika UNAND 7, no. 1 (2018): 33. http://dx.doi.org/10.25077/jmu.7.1.33-42.2018.

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Abstak. Tulisan ini membahas tentang metode penghitungan invers Moore-Penrose darimatriks A 2 Cmndengan rank(A) > 0. Metode yang digunakan adalah metode BenNoble.Teori yang diperlukan untuk penghitungan invers Moore-Penrose menggunakanmetode Ben-Noble adalah faktorisasi full rank dan partisi matriks.Kata Kunci: Invers Moore-Penrose, Faktorisasi Full Rank, Matriks Partisi

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10

Dincic, Nebojsa. "Extending the Moore-Penrose inverse." Filomat 30, no. 2 (2016): 419–28. http://dx.doi.org/10.2298/fil1602419d.

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We show that it is possible to define generalized inverse similar to the Moore-Penrose inverse by slightly modified Penrose equations. Then we are Investigating properties of this, so-called extended Moore-Penrose inverse.

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11

Wigantono, Sri, Moh Nurul Huda, Qonita Qurrota A'yun, Hardina Sandariria, Dimas Raditya Sahputra, and Tuhfatul Janan. "INVERS MOORE-PENROSE SEBAGAI REPRESENTASI MATRIKS PROYEKSI ORTHOGONAL." MAp (Mathematics and Applications) Journal 5, no. 1 (2023): 1–8. https://doi.org/10.15548/map.v5i1.6187.

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The inverse of matrix is one of the important properties of matrix. This properies, especially singular matrix, has been developed by Moore and continued by Penrose. Then, this inverse called Moore-Penrose inverse. The Moore-Penrose invers criteria can represent a projection on a vector space V along W with V and W are orthogonal to each other or can written with W=V^⊥ which is called orthogonal projection matrix on V. This research will present lemmas and theorems related to the Moore-Penrose invers construction of the multiplication matrix. Then, a square matrix is an orthogonal projection m

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12

Xu, Sanzhang, and Jianlong Chen. "The Moore-Penrose inverse in rings with involution." Filomat 33, no. 18 (2019): 5791–802. http://dx.doi.org/10.2298/fil1918791x.

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Let R be a unital ring with involution. In this paper, we first show that for an element a 2 R, a is Moore-Penrose invertible if and only if a is well-supported if and only if a is co-supported. Moreover, several new necessary and sufficient conditions for the existence of the Moore-Penrose inverse of an element in a ring R are obtained. In addition, the formulae of the Moore-Penrose inverse of an element in a ring are presented.

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13

Pablos Romo, Fernando, and Víctor Cabezas Sánchez. "Moore-Penrose inverse of some linear maps on infinite-dimensional vector spaces." Electronic Journal of Linear Algebra 36, no. 36 (2020): 570–86. http://dx.doi.org/10.13001/ela.2020.4979.

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The aim of this work is to characterize linear maps of infinite-dimensional inner product spaces where the Moore-Penrose inverse exists. This MP inverse generalizes the well-known Moore-Penrose inverse of a matrix $A\in \text{Mat}_{n\times m} ({\mathbb C})$. Moreover, a method for the computation of the MP inverse of some endomorphisms on infinite-dimensional vector spaces is given. As an application, the least norm solution of an infinite linear system from the Moore-Penrose inverse offered is studied.

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14

Sun, Yunhu, and Long Wang. "A note on the Moore-Penrose inverse of block matrices." Filomat 37, no. 1 (2023): 173–77. http://dx.doi.org/10.2298/fil2301173s.

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Motivated by the representation for the Moore-Penrose inverse of the block matrix over a *-regular ring presented in [R.E. Hartwig and P. Patr?cio, When does the Moore-Penrose inverse flip? Operators and Matrices, 6(1):181-192, 2012], we show that the formula of the Moore-Penrose inverse is the same as the expression given by [Nieves Castro-Gonz?lez, Jianlong Chen and Long Wang, Further results on generalized inverses in rings with involution, Elect. J. Linear Algebra, 30:118-134, 2015].

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15

Ji, Jun, and Yimin Wei. "The outer generalized inverse of an even-order tensor." Electronic Journal of Linear Algebra 36, no. 36 (2020): 599–615. http://dx.doi.org/10.13001/ela.2020.5011.

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Necessary and sufficient conditions for the existence of the outer inverse of a tensor with the Einstein product are studied. This generalized inverse of a tensor unifies several generalized inverses of tensors introduced recently in the literature, including the weighted Moore-Penrose, the Moore-Penrose, and the Drazin inverses. The outer inverse of a tensor is expressed through the matrix unfolding of a tensor and the tensor folding. This expression is used to find a characterization of the outer inverse through group inverses, establish the behavior of outer inverse under a small perturbati

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16

Castro-Gonzalez, Nieves, and Robert Hartwig. "Perturbation results and the forward order law for the Moore-Penrose inverse of a product." Electronic Journal of Linear Algebra 34 (February 21, 2018): 514–25. http://dx.doi.org/10.13001/1081-3810.3365.

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New expressions are given for the Moore-Penrose inverse of a product $AB$ of two complex matrices. Furthermore, an expression for $(AB)\dg - B\dg A\dg$ for the case where $A$ or $B$ is of full rank is provided. Necessary and sufficient conditions for the forward order law for the Moore-Penrose inverse of a product to hold are established. The perturbation results presented in this paper are applied to characterize some mixed-typed reverse order laws for the Moore-Penrose inverse, as well as the reverse order law.

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17

Suroto, Suroto, Najmah Istikaanah, and Sri Maryani. "APLIKASI DEKOMPOSISI RANK PADA PEMBENTUKAN INVERS MOORE-PENROSE MATRIKS ATAS ALJABAR MAX-PLUS TERSIMETRI." Teorema: Teori dan Riset Matematika 8, no. 1 (2023): 88. http://dx.doi.org/10.25157/teorema.v8i1.8029.

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Pada makalah ini dibahas tentang penggunaan dekomposisi rank untuk mengonstruksi invers Moore-Penrose pada matriks atas aljabar max-plus tersimetri. Penentuan eksistensi dekomposisi rank dilakukan dengan memanfaatkan suatu fungsi yang mengkorespondensikan aljabar max-plus tersimetri dengan aljabar konvensional. Selanjutnya, dengan memanfaatkan eksistensi invers setimbang, hasil dekomposisi rank ini digunakan untuk mengonstruksi bentuk invers Moore-Penrose dari matriks. Hasil yang diperoleh adalah bentuk invers Moore-Penrose dari suatu matriks atas aljabar max-plus tersimetri berdasarkan dekomp

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18

Cockett, Robin, and Jean-Simon Pacaud Lemay. "Moore-Penrose Dagger Categories." Electronic Proceedings in Theoretical Computer Science 384 (August 23, 2023): 171–86. http://dx.doi.org/10.4204/eptcs.384.10.

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19

Imori, Shinpei, and Dietrich Von Rosen. "On the mean and dispersion of the Moore-Penrose generalized inverse of a Wishart matrix." Electronic Journal of Linear Algebra 36, no. 36 (2020): 124–33. http://dx.doi.org/10.13001/ela.2020.5091.

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The Moore-Penrose inverse of a singular Wishart matrix is studied. When the scale matrix equals the identity matrix the mean and dispersion matrices of the Moore-Penrose inverse are known. When the scale matrix has an arbitrary structure no exact results are available. The article complements the existing literature by deriving upper and lower bounds for the expectation and an upper bound for the dispersion of the Moore-Penrose inverse. The results show that the bounds become large when the number of rows (columns) of the Wishart matrix are close to the degrees of freedom of the distribution.

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20

Tian, Yongge. "On mixed-type reverse-order laws for the Moore-Penrose inverse of a matrix product." International Journal of Mathematics and Mathematical Sciences 2004, no. 58 (2004): 3103–16. http://dx.doi.org/10.1155/s0161171204301183.

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Some mixed-type reverse-order laws for the Moore-Penrose inverse of a matrix product are established. Necessary and sufficient conditions for these laws to hold are found by the matrix rank method. Some applications and extensions of these reverse-order laws to the weighted Moore-Penrose inverse are also given.

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21

Ningsih, Sri Rahayu, Nova Noliza Bakar, and Monika Rianti Helmi. "g-INVERS KUADRAT TERKECIL, g-INVERS NORM MINIMUM, dan INVERS MOORE PENROSE." Jurnal Matematika UNAND 7, no. 2 (2018): 204. http://dx.doi.org/10.25077/jmu.7.2.204-211.2018.

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Abstrak. Generalisasi invers (g-invers) adalah salah satu jenis invers matriks. Tidakhanya pada matriks biasa, g-invers juga berlaku pada matriks fuzzy. Untuk setiap ma-triks fuzzy A berukuran m n, terdapat matriks X 2 Fnm sehingga memenuhi bebe-rapa persamaan Penrose. Matriks X 2 Fnm dikatakan g-invers dari A, jika X minimalmemenuhi persamaan yang pertama dari persamaan Penrose yaitu AXA = A denganmenggunakan operasi penjumlahan dan perkalian pada matriks fuzzy. Pada jurnal inidibahas bagaimana sifat-sifat dari g-invers kuadrat terkecil, g-invers norm minimum,dan invers Moore Penrose pada mat

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22

Li, Wende, Jianlong Chen, Yukun Zhou, and Xiaofeng Chen. "Weighted generalized invertibility in two semigroups of a ring with involution." Filomat 38, no. 15 (2024): 5261–74. https://doi.org/10.2298/fil2415261l.

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Let R be a ring with an involution and p ? R be a weighted projection. We characterize the relation between the weighted Moore-Penrose invertibility (resp., weighted pseudo core invertibility) of the corresponding elements of the two semigroups pRp and pRp + 1-p. As an application, we obtain the relation between the weighted Moore-Penrose invertibility (resp., weighted pseudo core invertibility) of the corresponding elements of the matrix semigroup AA? M,N Rm?m AA?M,N + Im-AA?M,N and the matrix semigroup A?M,N ARn?n A?M,N A + In-A?M,N A, where A ? Rm?n be weighted Moore-Penrose invertible with

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23

Wahyuni, Melati Sri, Nova Noliza Bakar, and Yanita Yanita. "SIFAT-SIFAT YANG TERKAIT DENGAN MATRIKS IDEMPOTEN." Jurnal Matematika UNAND 8, no. 1 (2019): 201. http://dx.doi.org/10.25077/jmu.8.1.201-208.2019.

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Suatu matriks A berukuran n × n dikatakan matriks idempoten jika A2 = A. Tulisan ini membahas tentang sifat-sifat yang terkait dengan matriks idempoten yang meliputi keterkaitan antara matriks idempoten dengan matriks ortogonal, simetri, involutori, dan invers Moore Penrose, serta membahas sifat-sifat ruang kolom, ruang null, rank dan trace dari matriks tersebut.Kata Kunci: Matriks Idempoten, Invers Moore-Penrose, Rank

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24

DAMM, TOBIAS, and HARALD K. WIMMER. "A CANCELLATION PROPERTY OF THE MOORE–PENROSE INVERSE OF TRIPLE PRODUCTS." Journal of the Australian Mathematical Society 86, no. 1 (2009): 33–44. http://dx.doi.org/10.1017/s144678870800044x.

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AbstractWe study the matrix equation C(BXC)†B=X†, where X† denotes the Moore–Penrose inverse. We derive conditions for the consistency of the equation and express all its solutions using singular vectors of B and C. Applications to compliance matrices in molecular dynamics, to mixed reverse-order laws of generalized inverses and to weighted Moore–Penrose inverses are given.

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25

Meenakshi, Ar, and N. Anandam. "On polynomialEPrmatrices." International Journal of Mathematics and Mathematical Sciences 15, no. 2 (1992): 261–66. http://dx.doi.org/10.1155/s0161171292000334.

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This paper gives a characterization ofEPr-λ-matrices. Necessary and sufficient conditions are determined for (i) the Moore-Penrose inverse of anEPr-λ-matrix to be anEPr-λ-matrix and (ii) Moore-Penrose inverse of the product ofEPr-λ-matrices to be anEPr-λ-matrix. Further, a condition for the generalized inverse of the product ofλ-matrices to be aλ-matrix is determined.

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26

Pajor, Anna. "A Note on the UEK Method." Barometr Regionalny. Analizy i Prognozy 15, no. 3 (2018): 7–10. http://dx.doi.org/10.56583/br.420.

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The paper concerns certain pitfalls of using the Moore-Penrose pseudoinverse for estimating regression coefficients in linear regression models when the matrix of explanatory variables has not full column rank. The aim of the paper is to show that in this case estimator of parameters based on the Moore-Penrose pseudoinverse is biased, and the bias leads to biased forecasts.

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27

Manjunatha Prasad, K., and R. B. Bapat. "The generalized Moore-Penrose inverse." Linear Algebra and its Applications 165 (March 1992): 59–69. http://dx.doi.org/10.1016/0024-3795(92)90229-4.

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28

Kyrchei, Ivan I. "Determinantal Representations of Solutions and Hermitian Solutions to Some System of Two-Sided Quaternion Matrix Equations." Journal of Mathematics 2018 (November 1, 2018): 1–12. http://dx.doi.org/10.1155/2018/6294672.

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Within the framework of the theory of quaternion row-column determinants previously introduced by the author, we derive determinantal representations (analogs of Cramer’s rule) of solutions and Hermitian solutions to the system of two-sided quaternion matrix equations A1XA1⁎=C1 and A2XA2⁎=C2. Since the Moore-Penrose inverse is a necessary tool to solve matrix equations, we use determinantal representations of the Moore-Penrose inverse previously obtained by the theory of row-column determinants.

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29

Udjiani, Titi, Suryoto Suryoto, and Harjito Harjito. "NORMAL ELEMENT ON IDENTIFY PROPERTIES." Journal of Fundamental Mathematics and Applications (JFMA) 1, no. 2 (2018): 95. http://dx.doi.org/10.14710/jfma.v1i2.16.

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Abstract. One type of element in the ring with involution is normal element. Their main properties is commutative with their image by involution in ring. Group invers of element in ring is always commutative with element which is commutative with itself. In this paper, properties of normal element in ring with involution which also have generalized Moore Penrose invers are constructed by using commutative property of group invers in ring. Keywords: Normal, Moore Penrose, group, involution

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30

Chien, Mao-Ting. "Numerical Range of Moore–Penrose Inverse Matrices." Mathematics 8, no. 5 (2020): 830. http://dx.doi.org/10.3390/math8050830.

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Let A be an n-by-n matrix. The numerical range of A is defined as W ( A ) = { x * A x : x ∈ C n , x * x = 1 } . The Moore–Penrose inverse A + of A is the unique matrix satisfying A A + A = A , A + A A + = A + , ( A A + ) * = A A + , and ( A + A ) * = A + A . This paper investigates the numerical range of the Moore–Penrose inverse A + of a matrix A, and examines the relation between the numerical ranges W ( A + ) and W ( A ) .

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31

Kelathaya, Umashankara, and Manjunatha Prasad Karantha. "Reverse order law for outer inverses and Moore-Penrose inverse in the context of star order." F1000Research 11 (July 27, 2022): 843. http://dx.doi.org/10.12688/f1000research.123411.1.

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The reverse order law for outer inverses and the Moore-Penrose inverse is discussed in the context of associative rings. A class of pairs of outer inverses that satisfy reverse order law is determined. The notions of left-star and right-star orders have been extended to the case of arbitrary associative rings with involution and many of their interesting properties are explored. The distinct behavior of projectors in association with the star, right-star, and left-star partial orders led to several equivalent conditions for the reverse order law for the Moore-Penrose inverse.

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32

Be, Aaisha, Vaibhav Shekhar, and Debasisha Mishra. "Numerical range for weighted Moore-Penrose inverse of tensor." Electronic Journal of Linear Algebra 40 (January 30, 2024): 140–71. http://dx.doi.org/10.13001/ela.2024.8143.

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This article first introduces the notion of weighted singular value decomposition (WSVD) of a tensor via the Einstein product. The WSVD is then used to compute the weighted Moore-Penrose inverse of an arbitrary-order tensor. We then define the notions of weighted normal tensor for an even-order square tensor and weighted tensor norm. Finally, we apply these to study the theory of numerical range for the weighted Moore-Penrose inverse of an even-order square tensor and exploit its several properties. We also obtain a few new results in matrix setting.

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33

Bürgisser, Peter, and Felipe Cucker. "Smoothed Analysis of Moore–Penrose Inversion." SIAM Journal on Matrix Analysis and Applications 31, no. 5 (2010): 2769–83. http://dx.doi.org/10.1137/100782954.

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34

Patrı́cio, Pedro, and Roland Puystjens. "Drazin–Moore–Penrose invertibility in rings." Linear Algebra and its Applications 389 (September 2004): 159–73. http://dx.doi.org/10.1016/j.laa.2004.04.006.

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35

Mary, Xavier. "Moore-Penrose Inverse in Kreĭn Spaces." Integral Equations and Operator Theory 60, no. 3 (2008): 419–33. http://dx.doi.org/10.1007/s00020-008-1562-0.

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36

Sheng, Xingping, and Guoliang Chen. "The generalized weighted Moore-Penrose inverse." Journal of Applied Mathematics and Computing 25, no. 1-2 (2007): 407–13. http://dx.doi.org/10.1007/bf02832365.

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37

Miao, Jianming, and Adi Ben-Israel. "Minors of the Moore-Penrose inverse." Linear Algebra and its Applications 195 (December 1993): 191–207. http://dx.doi.org/10.1016/0024-3795(93)90264-o.

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38

Jensen, D. R. "Minimal properties of Moore-Penrose inverses." Linear Algebra and its Applications 196 (January 1994): 175–82. http://dx.doi.org/10.1016/0024-3795(94)90322-0.

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39

Leiva, Hugo, and Raúl Manzanilla. "Moore-Penrose Inverse and Semilinear Equations." Advances in Linear Algebra & Matrix Theory 08, no. 01 (2018): 11–17. http://dx.doi.org/10.4236/alamt.2018.81002.

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40

Udjiani SRRM, Titi. "ELEMEN SIMETRIS DAN SIMETRIS DIPERUMUM PADA RING DENGAN INVOLUSI." Journal of Fundamental Mathematics and Applications (JFMA) 2, no. 2 (2019): 58. http://dx.doi.org/10.14710/jfma.v2i2.34.

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The definition of symmetric element in a ring with unity and equipped with involution can be generalized to generalized symmetric elements. But the properties of symmetric element not automatically can be generalized to generalized symmetric elements. In this paper, we discuss the property of symmetric element which can or cannot be generalized to generalized symmetric elements. Because of at least there is an element of symmetric and generalized symmetric elements which have the generalized Moore Penrose inverse, so method in this paper is by establishing a relationship between symmetric elem

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41

Malik, Saroj, and Néstor Thome. "On a revisited Moore-Penrose inverse of a linear operator on Hilbert spaces." Filomat 31, no. 7 (2017): 1927–31. http://dx.doi.org/10.2298/fil1707927m.

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For two given Hilbert spaces H and K and a given bounded linear operator A ? L(H,K) having closed range, it is well known that the Moore-Penrose inverse of A is a reflexive g-inverse G ? L(K,H) of A which is both minimum norm and least squares. In this paper, weaker equivalent conditions for an operator G to be the Moore-Penrose inverse of A are investigated in terms of normal, EP, bi-normal, bi-EP, l-quasi-normal and r-quasi-normal and l-quasi-EP and r-quasi-EP operators.

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42

Zhu, Huihui, and Yuxuan Yang. "On (B,C)-MP-inverses of rectangular matrices." Filomat 38, no. 3 (2024): 811–19. http://dx.doi.org/10.2298/fil2403811z.

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For any A ? Cn?m, the set of all n by m complex matrices, Mosic and Stanimirovic [14] introduced the composite OMP inverse of A by its outer inverse with the prescribed range, null space and Moore-Penrose inverse. This inverse unifies the core inverse, DMP inverse and Moore-Penrose inverse. In this paper, we mainly introduce and investigate a class of generalized inverses in complex matrices. Also, it is proved that this generalized inverse coincides with the OMP inverse. Finally, the defined inverse is related to OMP-inverses, W-core inverses and (b, c)-core inverses in the context of matrice

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Jabbarzadeh, M. R., and Jafari Bakhshkandi. "Centered operators via Moore-Penrose inverse and Aluthge transformations." Filomat 31, no. 20 (2017): 6441–48. http://dx.doi.org/10.2298/fil1720441j.

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Stanojević, Vukašin, Lev Kazakovtsev, Predrag S. Stanimirović, Natalya Rezova, and Guzel Shkaberina. "Calculating the Moore–Penrose Generalized Inverse on Massively Parallel Systems." Algorithms 15, no. 10 (2022): 348. http://dx.doi.org/10.3390/a15100348.

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In this work, we consider the problem of calculating the generalized Moore–Penrose inverse, which is essential in many applications of graph theory. We propose an algorithm for the massively parallel systems based on the recursive algorithm for the generalized Moore–Penrose inverse, the generalized Cholesky factorization, and Strassen’s matrix inversion algorithm. Computational experiments with our new algorithm based on a parallel computing architecture known as the Compute Unified Device Architecture (CUDA) on a graphic processing unit (GPU) show the significant advantages of using GPU for l

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Mond, B., and J. E. Pecaric. "On matrix convexity of the Moore-Penrose inverse." International Journal of Mathematics and Mathematical Sciences 19, no. 4 (1996): 707–10. http://dx.doi.org/10.1155/s0161171296000968.

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Taoudi, Mohamed Aziz. "On a Generalization of Partial Isometries in Banach Spaces." gmj 15, no. 1 (2008): 177–88. http://dx.doi.org/10.1515/gmj.2008.177.

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Abstract This paper is concerned with the definition and study of semipartial isometries on Banach spaces. This class of operators, which is a natural generalization of partial isometries from Hilbert to general Banach spaces, contains in particular the class of partial isometries recently introduced by M. Mbekhta [Acta Sci. Math. (Szeged) 70: 767–781, 2004]. First of all, we establish some basic properties of semi-partial isometries. Next, we introduce the notion of pseudo Moore–Penrose inverse as a natural generalization of the Moore–Penrose inverse from Hilbert spaces to arbitrary Banach sp

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Ragala, Ramesh, and G. Bharadwaja Kumar. "Recursive Block LU Decomposition based ELM in Apache Spark." Journal of Intelligent & Fuzzy Systems 39, no. 6 (2020): 8205–15. http://dx.doi.org/10.3233/jifs-189141.

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Due to the massive memory and computational resources required to build complex machine learning models on large datasets, many researchers are employing distributed environments for training the models on large datasets. The parallel implementations of Extreme Learning Machine (ELM) with many variants have been developed using MapReduce and Spark frameworks in the recent years. However, these approaches have severe limitations in terms of Input-Output (I/O) cost, memory, etc. From the literature, it is known that the complexity of ELM is directly propositional to the computation of Moore-Penr

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Jabbarzadeh, M. R., and M. Sohrabi Chegeni. "Moore-Penrose inverse of conditional type operators." Operators and Matrices, no. 1 (2017): 289–99. http://dx.doi.org/10.7153/oam-11-19.

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Hakopian, Yu R., and S. S. Aleksanyan. "MOORE–PENROSE INVERSE OF BIDIAGONAL MATRICES. III." Proceedings of the YSU A: Physical and Mathematical Sciences 50, no. 1 (239) (2016): 12–21. http://dx.doi.org/10.46991/psyu:a/2016.50.1.012.

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The present paper is a direct continuation of the papers [1, 2]. We obtain intermediate results, which will be used in the next final fourth part of this study, where a definitive solution to the Moore–Penrose inversion problem for singular upper bidiagonal matrices is given.

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Hakobyan, Yu R., and S. S. Aleksanyan. "MOORE–PENROSE INVERSE OF BIDIAGONAL MATRICES. IV." Proceedings of the YSU A: Physical and Mathematical Sciences 50, no. 2 (240) (2016): 28–34. http://dx.doi.org/10.46991/psyu:a/2016.50.2.028.

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The present work completes a research started in the papers [1–3]. Based on the results obtained in the previous papers, here we give a definitive solution to the problem of the Moore–Penrose inversion of singular upper bidiagonal matrices.

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