On the generalized bi (skew-) symmetric solutions of a linear matrix equation and its procrust problems.

Abstract: In this paper, the solvability conditions and the explicit expressions of the generalized bisymmetric and bi-skew-symmetric solutions of the matrix equation are respectively established by applying two methods. Then the maximal and minimal ranks of the solutions are derived. If the solvability conditions are not satisfied, the generalized bisymmetric and bi-skew-symmetric least squares solutions of the matrix equation are considered, and the generalized bisymmetric and bi-skew-symmetric least squares solutions with the minimum norm are also obtained. In addition, two algorithms are provided to compute the generalized bi (skew-) symmetric least squares solution, and some examples are given to illustrate that the algorithms are feasible. [Copyright &y& Elsevier]