Results 161 to 170 of about 640 (203)

An improvement on perturbation bounds for the Drazin inverse

Numerical Linear Algebra With Applications, 2003
AbstractThe Drazin inverse of a square matrix occurs in a number of applications. It is of importance to analyse the perturbation bounds for the Drazin inverse of a matrix. Let B=A+E. Under the assumption of rank(Bj) =rank(Ak), where j and k are the indices of B and A, respectively, upper bounds of ∥BD‐AD∥/∥AD∥ and ∥BBD‐AAD∥/∥AAD∥ have been recently ...
Yimin Wei, Xiezhang Li
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A Characterization and Representation of the Drazin Inverse

SIAM Journal on Matrix Analysis and Applications, 1996
Let \(A\) be a complex \(n\times n\) matrix. The index of \(A\) is the least integer \(k\) such that \(\text{rank}(A^k)=\text{rank}(A^{k+1})\). If \(A\) has rank \(k\), then the Drazin inverse is the unique \(n\times n\) matrix such that \(A^{k+1}X=A^k\), \(XAX=X\) and \(AX=XA\).
Wei Yimin
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The Drazin inverse of a modified matrix

Applied Mathematics and Computation, 2002
The author gives explicit formulas for the Drazin inverse of matrices \(A-BC\) under assumptions such as \((I-AA^D)C=0,B(I-A^DA)=0\).
Yimin Wei
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A characterization for the W-weighted Drazin inverse and a Cramer rule for the W-weighted Drazin inverse solution

Applied Mathematics and Computation, 2002
The paper presents a characterization for the W-weighted Drazin inverse, and a Cramer rule for W-weighted Drazin inverse solution of a singular linear equation.
Yimin Wei
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Weighted extended g-Drazin inverse

Aequationes Mathematicae, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dijana Mosić, Mosić Dijana
exaly   +3 more sources

An expression of the Drazin inverse of a perturbed matrix

Applied Mathematics and Computation, 2004
It is well-known that the perturbation theory of the Drazin inverse \(A^D\) is much more complicated than that of the group inverse \(A^{\sharp}\), which coincides with \(A^D\) in the case where ind\((A)=1\). The constraint ind\((A)=1\) allows to achieve some good upper bounds on relative perturbation error.
Xiezhang Li, Yimin Wei 0001
openaire   +4 more sources

Some additive results on Drazin inverse [PDF]

Applied Mathematics, 2015
In this paper, we investigate additive results of the Drazin inverse of elements in a ring R. Under the condition ab = ba, we show that a + b is Drazin invertible if and only if aa^D(a+b) is Drazin invertible, where the superscript D means the Drazin ...
Julio Benitez
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New additive results for the generalized Drazin inverse

Journal of Mathematical Analysis and Applications, 2010
In this paper, we investigate additive properties of generalized Drazin inverse of two Drazin invertible linear operators in Banach spaces. Under the commutative condition of PQ=QP, we give explicit representations of the generalized Drazin inverse (P+Q ...
Yimin Wei
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