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The skew-symmetric orthogonal solutions of the matrix equation AX=B
- Source :
-
Linear Algebra & its Applications . Jun2005, Vol. 402, p303-318. 16p. - Publication Year :
- 2005
-
Abstract
- Abstract: An n×n real matrix X is said to be a skew-symmetric orthogonal matrix if XT=−X and XTX=I. Using the special form of the C–S decomposition of an orthogonal matrix with skew-symmetric k×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. [Copyright &y& Elsevier]
- Subjects :
- *SYMMETRIC matrices
*UNIVERSAL algebra
*ALGORITHMS
*MATHEMATICAL analysis
Subjects
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 402
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 17059110
- Full Text :
- https://doi.org/10.1016/j.laa.2005.01.022