Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9498210 | Linear Algebra and its Applications | 2005 | 16 Pages |
Abstract
An n Ã n real matrix X is said to be a skew-symmetric orthogonal matrix if XT = âX and XTX = I. Using the special form of the C-S decomposition of an orthogonal matrix with skew-symmetric k Ã k leading principal submatrix, this paper establishes the necessary and sufficient conditions for the existence of and the expressions for the skew-symmetric orthogonal solutions of the matrix equation AX = B. In addition, in corresponding solution set of the equation, the explicit expression of the nearest matrix to a given matrix in the Frobenius norm have been provided. Furthermore, the Procrustes problem of skew-symmetric orthogonal matrices is considered and the formula solutions are provided. Finally an algorithm is proposed for solving the first and third problems. Numerical experiments show that it is feasible.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Chunjun Meng, Xiyan Hu, Lei Zhang,