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廣義對(duì)稱(chēng)、反對(duì)稱(chēng)矩陣反問(wèn)題
廣義對(duì)稱(chēng)、反對(duì)稱(chēng)矩陣反問(wèn)題
摘要
本文定義了實(shí)數(shù)域R上的兩類(lèi)廣義對(duì)稱(chēng)和反對(duì)稱(chēng)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(lèi)廣義對(duì)稱(chēng)和反對(duì)稱(chēng)矩陣集合中矩陣反問(wèn)題AX=B有解的充分必要條件及有解時(shí)解的1般表達(dá)式．
關(guān)鍵詞：廣義對(duì)稱(chēng)矩陣；廣義反對(duì)稱(chēng)矩陣；廣義奇異值分解；最佳逼近；反問(wèn)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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