Volume no :1, Issue no: 3, December 2008

ANTI-SYMMETRIC ORTHOGONAL ANTI-SYMMETRIC SOLUTIONS OF MATRIX EQUATION AND THE OPTIMAL APPROXIMATION

Author's: Lan Yan and Peng Xiangyang
Pages: [533] - [546]
Received Date: May 14, 2008
Submitted by:

Abstract

An real P is said to be an anti-symmetric orthogonal matrix if and An real X is said to be an anti-symmetric orthogonal anti-symmetric matrix with respect to the symmetric orthogonal-matrix P if and By applying the generalized singular value decomposition (GSVD) of matrices, this paper provides the necessary and sufficient conditions for the existence and the expression for the anti-symmetric orthogonal anti-symmetric with a symmetric orthogonal matrix P solutions of the matrix equation In addition, in solution set of the equation, the expression of the optimal approximation solution to the given matrix and of least-norm solution are derived.

Keywords

matrix equation, symmetric orthogonal anti-symmetric matrices, optimal approximation, least-norm solution.