Results 1 to 10 of about 672 (66)
Displacement structure of the DMP inverse
Open Mathematics, 2022 A matrix AA is said to have the displacement structure if the rank of the Sylvester displacement AU−VAAU-VA or the Stein displacement A−VAUA-VAU is much smaller than the rank of AA.
Zhong Jin, Yang Hong
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Characterizations of the group invertibility of a matrix revisited
Demonstratio Mathematica, 2022 A square complex matrix AA is said to be group invertible if there exists a matrix XX such that AXA=AAXA=A, XAX=XXAX=X, and AX=XAAX=XA hold, and such a matrix XX is called the group inverse of AA.
Tian Yongge
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The group inverse of circulant matrices depending on four parameters
Special Matrices, 2021 Explicit expressions for the coefficients of the group inverse of a circulant matrix depending on four complex parameters are analytically derived. The computation of the entries of the group inverse are now reduced to the evaluation of a polynomial ...
Carmona A. +3 more
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The dual index and dual core generalized inverse
Open Mathematics, 2023 In this article, we introduce the dual index and dual core generalized inverse (DCGI). By applying rank equation, generalized inverse, and matrix decomposition, we give several characterizations of the dual index when it is equal to 1. We realize that if
Wang Hongxing, Gao Ju
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W-MPD–N-DMP-solutions of constrained quaternion matrix equations
Special Matrices, 2023 The solvability of several new constrained quaternion matrix equations is investigated, and their unique solutions are presented in terms of the weighted MPD inverse and weighted DMP inverse of suitable matrices.
Kyrchei Ivan I. +2 more
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Idempotent operator and its applications in Schur complements on Hilbert C*-module
Special Matrices, 2023 The present study proves that TT is an idempotent operator if and only if R(I−T∗)⊕R(T)=X{\mathcal{ {\mathcal R} }}\left(I-{T}^{\ast })\oplus {\mathcal{ {\mathcal R} }}\left(T)={\mathcal{X}} and (T∗T)†=(T†)2T{\left({T}^{\ast }T)}^{\dagger }={\left({T ...
Karizaki Mehdi Mohammadzadeh +1 more
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Bordering method to compute Core-EP inverse
Special Matrices, 2018 Following the work of Kentaro Nomakuchi[10] and Manjunatha Prasad et.al., [7] which relate various generalized inverses of a given matrix with suitable bordering,we describe the explicit bordering required to obtain core-EP inverse, core-EP generalized ...
Prasad K. Manjunatha, Raj M. David
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On mixed‐type reverse‐order laws for the Moore‐Penrose inverse of a matrix product
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 58, Page 3103-3116, 2004., 2004 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.
Yongge Tian
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Diagonal dominance and invertibility of matrices
Special Matrices, 2023 A weakly diagonally dominant matrix may or may not be invertible. We characterize, in terms of combinatorial structure and sign pattern when such a matrix is invertible, which is the common case. Examples are given.
Johnson Charles Royal +2 more
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On the relation between Moore′s and Penrose′s conditions
International Journal of Mathematics and Mathematical Sciences, Volume 30, Issue 8, Page 505-509, 2002., 2002 Moore (1920) defined the reciprocal of any matrix over the complex field by three conditions, but the beauty of the definition was not realized until Penrose (1955) defined the same inverse using four conditions. The reciprocal is now often called the Moore-Penrose inverse, and has been widely used in various areas.
Gaoxiong Gan
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