Results 11 to 20 of about 790 (92)
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.
Yongge Tian
semanticscholar +2 more sources
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
doaj +1 more source
g-Drazin inverses for operator matrices
, 2020 Additive results for the generalized Drazin inverse of Banach space operators are presented. Suppose the bounded linear operators a and b on an arbitrary complex Banach space have generalized Drazin inverses.
Huanzhen Chen, M. Abdolyousefi
semanticscholar +1 more source
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
doaj +1 more source
An Infinite Dimensional Approach to the Third Fundamental Theorem of Lie [PDF]
, 2008 We revisit the third fundamental theorem of Lie (Lie III) for finite dimensional Lie algebras in the context of infinite dimensional matrices.Comment: This is a contribution to the Proc.
Bourgin, Richard D., Robart, Thierry P.
core +4 more sources
, 2020 One of the typical forms of linear matrix expressions (linear matrix-valued functions) is given by A + B1X1C1 + · · · + BkXkCk, where X1, . . . , Xk are independent variable matrices of appropriate sizes, which include almost all matrices with unknown ...
Yongge Tian
semanticscholar +1 more source
Left and right generalized Drazin invertible operators on Banach spaces and applications
Operators and Matrices, 2019 In this paper, left and right generalized Drazin invertible operators on Banach spaces are defined and characterized by means of the generalized Kato decomposition. Then, new binary relations associated with these operators are presented and studied.
D. E. Ferreyra, F. Levis, N. Thome
semanticscholar +1 more source
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
doaj +1 more source
Characteristic polynomial, determinant and inverse of a Fibonacci-Sylvester-Kac matrix
Special Matrices, 2021 In this paper, we consider a new Sylvester-Kac matrix, i.e., Fibonacci-Sylvester-Kac matrix. We discuss the eigenvalues, eigenvectors and characteristic polynomial of this matrix in two categories based on whether the Fibonacci-Sylvester-Kac matrix order
Jiang Zhaolin, Zheng Yanpeng, Li Tianzi
doaj +1 more source
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
wiley +1 more source