Displaying 141 – 160 of 229

Showing per page

The Re-nonnegative definite solutions to the matrix equation A X B = C

Qing Wen Wang, Chang Lan Yang (1998)

Commentationes Mathematicae Universitatis Carolinae

An n × n complex matrix A is called Re-nonnegative definite (Re-nnd) if the real part of x * A x is nonnegative for every complex n -vector x . In this paper criteria for a partitioned matrix to be Re-nnd are given. A necessary and sufficient condition for the existence of and an expression for the Re-nnd solutions of the matrix equation A X B = C are presented.

The Smith normal form of product distance matrices

R. B. Bapat, Sivaramakrishnan Sivasubramanian (2016)

Special Matrices

Let G = (V, E) be a connected graph with 2-connected blocks H1, H2, . . . , Hr. Motivated by the exponential distance matrix, Bapat and Sivasubramanian in [4] defined its product distance matrix DG and showed that det DG only depends on det DHi for 1 ≤ i ≤ r and not on the manner in which its blocks are connected. In this work, when distances are symmetric, we generalize this result to the Smith Normal Form of DG and give an explicit formula for the invariant factors of DG.

Currently displaying 141 – 160 of 229