## Symmetric and antipersymmetric extremal rank solutions for linear matrix equations and their approximation

### Volume 148 / 2017

Colloquium Mathematicum 148 (2017), 13-26
MSC: 15A29, 65F18.
DOI: 10.4064/cm6557-5-2016
Published online: 27 January 2017

#### Abstract

This study establishes solvability conditions and explicit expressions of symmetric and antipersymmetric solutions of a matrix equation $AX=B$. The maximal and minimal ranks of the solutions are then derived. Finally, the matrix closest to a given matrix in the Frobenius norm is given explicitly in the minimal rank solution set of the matrix equation $AX=B$.