廣義對稱、反對稱矩陣反問題

廣義對稱、反對稱矩陣反問題

廣義對稱、反對稱矩陣反問題

摘要

本文定義了實數域R上的兩類廣義對稱和反對稱矩陣集合．利用矩陣的Moore-Penrose廣義逆和廣義奇異值分解，給出了在所定義的兩類廣義對稱和反對稱矩陣集合中矩陣反問題AX=B有解的充分必要條件及有解時解的1般表達式．
關鍵詞：廣義對稱矩陣；廣義反對稱矩陣；廣義奇異值分解；最佳逼近；反問題

The Inverse Problem of Generalized Symmetric and Anti-symmetric Matrix

ABSTRACT

This paper two kinds of generalized symmetric and anti-symmetric matrix sets are defined. By applying the Moore-Penrose generalized inverse and the decomposition of generalized singular value of matrices, the necessary and sufficient condition for the inverse problem AX=B have a solution in given matrix sets are derived. And the general expression for the solution of the problem are also given.
Keywords: generalized symmetric matrix; generalized anti-symmetric matrix; the decomposition of generalized singular value; optimal approximation; inverse problem

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