Condition numbers of the minimum norm least squares solution for the least squares problem involving Kronecker products

In this paper, the upper bounds for two kinds of normiwse condition numbers are derived for $ \min\limits_{x}\|(A\otimes B)x-b\|_2 $ when the coefficient matrix is of rank deficient. In addition, the upper bounds on the mixed and componentwise condition numbers are also given. Numerical experiments are given to confirm our results.