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期刊论文
The skew-symmetric orthogonal solutionsof the matrix equation AX=B☆
Linear Algebra and its Applications 402 (2005) 303-318,-0001,():
An n×n real matrix X is said to be a skew-symmetric orthogonal matrix if XT=−Xand XTX =I. Using the special form of the C-S decomposition of an orthogonal matrixwith skew-symmetric k×k leading principal submatrix, this paper establishes the necessaryand sufficient conditions for the existence of and the expressions for the skew-symmetricorthogonal solutions of the matrix equation AX=B. In addition, in corresponding solutionset of the equation, the explicit expression of the nearest matrix to a given matrix in theFrobenius norm have been provided. Furthermore, the Procrustes problem of skew-symmetricorthogonal matrices is considered and the formula solutions are provided. Finally an algorithmis proposed for solving the first and third problems. Numerical experiments show that it isfeasible.
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