Weighted UDV∗-decomposition and weighted spectral decomposition for rectangular matrices and their applications

In this paper, the weighted UDV∗-decomposition theorem and the weighted spectral decomposition theorem for rectangular matrices are proved. Their applications are discussed, in which the matrix functions, Cauchy's formula for matrix functions, and the weighted resolvent equation of rectangular matrices are studied. In addition, we also present a solution of the matrix equation AXB = C.