论文信息 - Weighted UDV*-decomposition and weighted spectral decomposition for rectangular matrices and their applications

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.

Hu Yang | Hanyu Li

[1] C. Loan. Generalizing the Singular Value Decomposition , 1976 .

[2] Dingkun Wang. Some topics on weighted Moore-Penrose inverse, weighted least squares and weighted regularized Tikhonov problems , 2004, Appl. Math. Comput..

[3] Yimin Wei,et al. Condition numbers and perturbation of the weighted Moore-Penrose inverse and weighted linear least squares problem , 2003, Appl. Math. Comput..

[4] Adi Ben-Israel,et al. Generalized inverses: theory and applications , 1974 .

[5] A. Doma. Generalized Inverses of Matrices and Its Applications. , 1983 .

[6] Hu Yang,et al. Weighted Polar Decomposition and WGL Partial Ordering of Rectangular Complex Matrices , 2008, SIAM J. Matrix Anal. Appl..