Saroj B Malik

Matrix Partial Orders, Shorted Operators and Applications

Introduction Decompositions and Generalized Inverses Minus Order Sharp Order Star Order One-Sided Orders Lowner Order and Majorization Unified Theory of Matrix Partial Orders through Generalized Inverses Parallel Sums Schur Complements and Shorted Operators Shorted Operators II Supremum and Infimum for a Pair of Matrices Partial Orders for Modified Matrices Statistics Electrical Network Theory.

On a new generalized inverse for matrices of an arbitrary index

The purpose of this paper is to introduce a new generalized inverse, called DMP inverse, associated with a square complex matrix using its Drazin and Moore-Penrose inverses. DMP inverse extends the notion of core inverse, introduced by Baksalary and Trenkler for matrices of index at most 1 in (Baksalary and Trenkler (2010) [1]) to matrices of an arbitrary index. DMP inverses are analyzed from both algebraic as well as geometrical approaches establishing the equivalence between them.

Some more properties of core partial order

In this paper the core partial order introduced by Baksalary and Trenkler has been studied further. New characterizations of the core partial order have been derived. Relationship between the core partial order and some known partial orders has been also investigated.

The class of m-EP and m-normal matrices

The well-known classes of EP matrices and normal matrices are defined by the matrices that commute with their Moore–Penrose inverse and with their conjugate transpose, respectively. This paper investigates the class of m-EP matrices and m-normal matrices that provide a generalization of EP matrices and normal matrices, respectively, and analyses both of them for their properties and characterizations.

On a revisited Moore-Penrose inverse of a linear operator on Hilbert spaces

For two given Hilbert spaces H and K and a given bounded linear operator A \in L(H,K) having closed range, it is well known that the Moore-Penrose inverse of A is a reflexive 1-inverse G \in L(K,H) of A which is both minimum norm and least squares. In this paper, weaker equivalent conditions for an operator G to be the Moore-Penrose inverse of A are investigated in terms of normal, EP, bi-normal, bi-EP, l-quasi-normal and r-quasi-normal and l-quasi-EP and r-quasi-EP operators.