Rank constrained matrix best approximation problem with respect to (skew) Hermitian matrices

摘要

In this literature, we study a rank constrained matrix approximation problem in the Frobenius norm: minr(X)=k‖BXB∗−A‖F2, where k is a nonnegative integer, A and X are (skew) Hermitian matrices. By using the singular value decomposition and the spectrum decomposition, we derive some conditions for the existence of (skew) Hermitian solutions, and establish general forms for the (skew) Hermitian solutions to this matrix approximation problem.