On Least Squares Solutions of Matrix Equation MZN=S

¹ School of Mathematics and Science, Shijiazhuang University of Economics, Shijiazhuang, China

² School of Mathematics and Science, Shijiazhuang University of Economics, Shijiazhuang, China

³ School of Mathematics and Science, Shijiazhuang University of Economics, Shijiazhuang, China

Abstract

Let be a given Hermitian matrix satisfying . Using the eigenvalue decomposition of , we consider the least squares solutions to the matrix equation , with the constraint .

KeywordsMatrix EquationEigenvalue DecompositionCanonical Correlation DecompositionReflexive MatrixLeast Squares Solution

D. S. Cvetkovic-Ilic, “The Reflexive Solutions of the Matrix Equation ,” Computers & Mathematics with Applications, Vol. 51, 2006, pp. 897-902. http://dx.doi.org/10.1016/j.camwa.2005.11.032?
X. Y. Peng, X. Y. Hu and L. Zhang, “The Reflexive and Anti-Reflexive Solutions of the Matrix Equation ,” The Journal of Computational and Applied Mathematics, Vol. 200, 2007, pp. 749-760. http://dx.doi.org/10.1016/j.cam.2006.01.024
Y. X. Yuan and H. Dai, “Generalized Reflexive Solutions of the Matrix Equation and an Associated Optimal Approximation Problem,” Computers & Mathematics with Applications, Vol. 56, 2008, pp. 1643-1649. http://dx.doi.org/10.1016/j.camwa.2008.03.015
A. Herrero and N. Thome, “Using the GSVD and the Lifting Technique to Find Reflexive and Anti-Reflexive Solutions of ,” Applied Mathematics Letters, Vol. 24, 2011, pp. 1130-1141. http://dx.doi.org/10.1016/j.aml.2011.01.039
G. P. Xu, M. S. Wei and D. S. Zheng, “On Solutions of Matrix Equation ,” Linear Algebra and Its Applications, Vol. 279, 1998, pp. 93-100. http://dx.doi.org/10.1016/S0024-3795(97)10099-4

Menu

On Least Squares Solutions of Matrix Equation MZN=S

Abstract

References (5)