Results 11 to 20 of about 640 (203)
The Expression of the Generalized Drazin Inverse of A−CB [PDF]
Abstract and Applied Analysis, 2012 We investigate the generalized Drazin inverse of A−CB over Banach spaces stemmed from the Drazin inverse of a modified matrix and present its expressions under some conditions.
Xiaoji Liu, Dengping Tu, Yaoming Yu
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The (2,2,0) Drazin inverse problem [PDF]
Linear Algebra and its Applications, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Patrício, Pedro, Hartwig, Robert E.
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A characterization of the drazin inverse
Linear Algebra and its Applications, 2001 Given a square complex matrix \(A\) of order \(n\), the author shows that there exists a unique Drazin inverse \(Y\) of \(A\) under certain conditions involving the index of \(A\) and the rank of a composed matrix of order \(2n\) (first row: \(A\), \(AY\); second row: \(AY\), \(Y\)) that must be equal with \(\operatorname {rank}A\).
Zhang, Liping
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The Drazin inverse as a gradient
Linear Algebra and its Applications, 1984 If A is an invertible \(n\times n\) matrix, X an \(n\times n\) matrix variable, and \(| X| =\det X\), then \(\ell n | X|\) is differentiable near A and \(\nabla_ x\) \(\ell n | X|\) at \(X=A\) is \((A^{-1})^ T\). This paper examines various analogues and related questions for the Drazin inverse \(A^ d\).
Gabriel, Richard, Hartwig, Robert E.
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Jacobson’s lemma for the generalized Drazin inverse
Linear Algebra and its Applications, 2012 The authors investigate some properties of elements in a ring which admit the generalized Drazin inverse. It is shown that the element \(1-ab\) is generalized Drazin invertible if and only if so is \(1-ba\) and a formula for the generalized Drazin inverse of \(1-ba\) in terms of the generalized Drazin inverse and the spectral idempotent of \(1-ab\) is ...
Zhuang, Guifen +2 more
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An Improved Computationally Efficient Method for Finding the Drazin Inverse
Discrete Dynamics in Nature and Society, 2018 Drazin inverse is one of the most significant inverses in the matrix theory, where its computation is an intensive and useful task. The objective of this work is to propose a computationally effective iterative scheme for finding the Drazin inverse.
Haifa Bin Jebreen, Yurilev Chalco-Cano
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Theory and Applications of CategoriesDrazin inverses are a fundamental algebraic structure which have been extensively deployed in semigroup theory, ring theory, and matrix theory. Drazin inverses can also be defined for endomorphisms in any category. However, beyond a paper by Puystjens and Robinson from 1987, there has been almost no further development of Drazin inverses in category ...
Cockett, Robin +2 more
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Integral representations of the $g$-Drazin inverse in $C^*$-algebras [PDF]
, 2004 summary:The paper gives new integral representations of the $g$-Drazin inverse of an element $a$ of a $C^*$-algebra that require no restriction on the spectrum of $a$.
Wei, Yimin +2 more
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Some results on Drazin-Dagger matrices, reciprocal matrices, and conjugate EP matrices [PDF]
Journal of Mahani Mathematical ResearchIn this paper, a class of matrices, namely, Drazin-dagger matrices, in which the Drazin inverse andthe Moore-Penrose inverse commute, is introduced. Also, some properties of the generalized inverses of these matrices, are investigated.
Mahdiyeh Mortezaei +1 more
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The Characterizations of WG Matrix and Its Generalized Cayley–Hamilton Theorem
Journal of Mathematics, 2021 Based on the core-EP decomposition, we use the WG inverse, Drazin inverse, and other inverses to give some new characterizations of the WG matrix.
Na Liu, Hongxing Wang
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