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The Anti-Symmtric Orthogonal Anti-Symmetric Solutions of Matrix Equation and the Optimal Approximation

Lei Zhang

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Abstract

By applying the generalized singular value decomposition(GSVD) of matrices,this paper provdes 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 A~TXA=B(A∈~(n×m),B∈R~(m×m)).In addition,in the solution set of the equation,the expression of the optimal approximation solution to the given matrix and of minimum solution are derived.

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What this paper is about

By applying the generalized singular value decomposition(GSVD) of matrices,this paper provdes 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 A~TXA=B(A∈~(n×m),B∈R~(m×m)).In addition,in the solution set of the equation,the expression of the optimal approximation solution to the given matrix and of minimum solution are derived.

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Available abstract

By applying the generalized singular value decomposition(GSVD) of matrices,this paper provdes 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 A~TXA=B(A∈~(n×m),B∈R~(m×m)).In addition,in the solution set of the equation,the expression of the optimal approximation solution to the given matrix and of minimum solution are derived.

Key concepts: Mathematics, Symmetric matrix, Orthogonal matrix, Singular value decomposition, Matrix (chemical analysis), Mathematical analysis, Expression (computer science), Applied mathematics

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