Results 1 to 10 of about 790 (92)
Pairs of k-step reachability and m-step observability matrices
Special Matrices, 2013 Let $V$ and $W$ be matrices of size $ n \times pk$ and $q m \times n $, respectively. A necessary and sufficient condition is given for the existence of a triple $(A,B,C)$ such that $V$ a $k$-step reachability matrix of $(A,B)$ and $W$ an $m$-step ...
Ferrante Augusto, Wimmer Harald K.
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Special Matrices, 2015 In this paper we characterize Moore-Penrose inverses of Gram matrices leaving a cone invariant in an indefinite inner product space using the indefinite matrix multiplication. This characterization includes the acuteness (or obtuseness) of certain closed
Appi Reddy K., Kurmayya T.
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On the Drazin inverse and M-P inverse for sum of matrices
Operators and Matrices, 2021 Drazin inverse and M-P inverse have many important applications in the aspects of theoretic research of operator and statistics. In this article, we will exhibit under suitable conditions a neat relationship between the Drazin inverse of A + B and the ...
Yingying Qin, Zhiping Xiong, Wanna Zhou
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The g-Drazin inverses of special operator matrices
Operators and Matrices, 2021 An element a in a Banach algebra A has g-Drazin inverse provided that there exists b ∈ A such that b = bab , ab = ba , a− a2b ∈ A qnil . In this paper we give a computational formula for the g-Drazin inverse of operator matrix ( E I F 0 ) which was posed
Hua Chen, M. Abdolyousefi
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The Pseudo Drazin inverses in Banach Algebras
Communications in Mathematical Research, 2021 Let A be a complex Banach algebra and J be the Jacobson radical of A . (1) We firstly show that a is generalized Drazin invertible in A if and only if a+ J is generalized Drazin invertible in A /J. Then we prove that a is pseudo Drazin invertible in A if
Jianlong Chen
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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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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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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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Group inverse of finite potent endomorphisms on arbitrary vector spaces
, 2020 The aim of this work is to introduce the group inverse of a finite potent endomorphism on an infinite-dimensional vector space that generalizes the notion of group inverse of a square finite matrix. The existence and uniqueness of this inverse is proved,
F. P. Romo
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