On rank-constrained Hermitian nonnegative-definite least squares solutions to the matrix equation AXA~H = B

摘要

In the literature, rank-constrained Hermitian nonnegative-definite solutions to the matrix equation AXA~H = B have been investigated, under the conditions that B is Hermitian and nonnegative-definite, and the matrix equation is consistent. In this paper, we discuss rank-constrained Hermitian nonnegative-definite least squares solutions to this matrix equation, in which the above conditions may not hold. We derive the rank range and expression of these least squares solutions. Therefore, the results obtained in this paper generalize those in the literature.