We introduce some new algebraic and topological properties of the Minkowski inverse A([Symbol: see text) of an arbitrary matrix A[Symbol: see text] M m,n (including singular and rectangular) in a Minkowski space μ. Furthermore, we show that the Minkowski inverse A ([Symbol: see text]) in a Minkowski space and the Moore-Penrose inverse A(+) in a Hilbert space are different in many properties suc...

in this paper, we find explicit solution to the operator equation$txs^* -sx^*t^*=a$ in the general setting of the adjointable operators between hilbert $c^*$-modules, when$t,s$ have closed ranges and $s$ is a self adjoint operator.

Abstract. A well–known property of an irreducible non–singular M–matrix is that its inverse is non–negative. However, when the matrix is an irreducible and singular M–matrix it is known that it has a generalized inverse which is non–negative, but this is not always true for any generalized inverse. We focus here in characterizing when the Moore–Penrose inverse of a symmetric, singular, irreduci...

In this paper, we investigate the Sherman-Morrison-Woodbury formula for {1}-inverses and {2}-inverses of bounded linear operators on a Hilbert space. Some conditions are established to guarantee that (A+YGZ*)? = A? ?A?Y(G? +Z*A?Y)?Z*A? holds, where stands any kind standard inverse, {1}-inverse, {2}-inverse, Moore-Penrose Drazin group core inverse dual A.

The purpose of image encryption is to protect content from unauthorized access. Image encryption is usually done by pixel scrambling and confusion, so process is possible to reverse only by knowing secret information. In this paper we introduce a new method for digital image encryption, based on a 2D cellular automaton and pixel separation. Novelty in the proposed method lies in the application...

In this talk, we discuss the maximum number of n × n pure imaginary quaternionic solutions to the Hurwitz matrix equations given by T i T * j + T j T Abstract Let T be a bounded linear operator on a complex Hilbert space H. For 0 ≤ q ≤ 1, the