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Generalized Inverse of a Singular Matrix [PDF]

, 1963
J. C. KOOP
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On generalized inverses and Green’s relations

Linear Algebra and its Applications, 2011
We study generalized inverses on semigroups by means of Green's relations. We first define the notion of inverse along an element and study its properties. Then we show that the classical generalized inverses (group inverse, Drazin inverse and Moore-Penrose inverse) belong to this class.
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EP Operators and Generalized Inverses [PDF]

, 1975
Stephen L. Campbell, Carl D. Meyer
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Involutions for matrices and generalized inverses

Linear Algebra and its Applications, 1998
The author builds a linear complex algebra taking an arbitrary complex involution (i.e. an automorphism of the field \(\mathbb{C}\) of complex numbers of order two) instead of the ordinary conjugation. In the set \(M\) of all complex matrices an involution is defined as a map \(*:M\to M\) satisfying \((A^*)^* =A\) and \((AB)^* =B^*A^*\) in any possible
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The Reverse Order Law for the {1,3M,4N}—The Inverse of Two Matrix Products

Axioms
By using the maximal and minimal ranks of some generalized Schur complement, the equivalent conditions for the reverse order law (AB){1,3M,4K}=B{1,3N,4K}A{1,3M,4N} are presented.
Yingying Qin, Baifeng Qiu, Zhiping Xiong
doaj   +1 more source

An APL algorithm for finding the generalized inverse of a matrix [PDF]

, 1979
P. Sarachik, Ümi̇t Özgüner
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An Investigation on Mathematical Modeling of Operators on The Hilbert Domain subjected to The Equality Theory

Journal of Applied Science and Engineering
This work begins by presenting the essential and enough circumstances for the presence of the Hermitian solution to equations ΨXΦ + Φ∗YΨ∗ = Ω = Ψ∗XΦ∗+ ΦYΨ in the case where the operators are linear and bounded in a Hilbert space and in terms of the Moore-
Salim Dawood Mohsen, Ihsan Abdulsattar Awadh   +1 more
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Best Least Squares Solutions to Finite Difference Equations Using the Generalized Inverse and Tensor Product Methods [PDF]

, 1973
John F. Dalphin, V. Lovass‐Nagy
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Inverses of generalized Vandermonde matrices

Journal of Mathematical Analysis and Applications, 1988
The author obtains formulas for inverses of generalized Vandermonde matrices by using a method related to Horner's method for polynomials.
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Erratum: “The generalized inverse of a nonnegative matrix” [PDF]

, 1973
Robert J. Plemmons, Randall E. Cline
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