On Condition Numbers for the Weighted Moore-Penrose Inverse and the Weighted Least Squares Problem involving Kronecker Products

Abstract

We establish some explicit expressions for norm-wise, mixed and componentwise condition numbers for the weighted Moore-Penrose inverse of a matrix $A⊗B$ and more general matrix function compositions involving Kronecker products. The condition number for the weighted least squares problem (WLS) involving a Kronecker product is also discussed.