重庆工商大学学报：自然科学版
重慶工商大學學報：自然科學版
중경공상대학학보：자연과학판
Journal of Chongqing Technology and Business University:Natural Science Edition
2012年
2期
23-27
,共5页
正交矩阵%行反正交矩阵%行列对称矩阵
正交矩陣%行反正交矩陣%行列對稱矩陣
정교구진%행반정교구진%행렬대칭구진
orthogonal matrix%contrary orthogonal matrix%row （column） symmetric matrix
给出行反正交矩阵的概念，并讨论其行列式、可逆性、迹、特征值等问题，得到行反正交矩阵的行列式、逆矩阵、特征值与迹；并得出了以下主要结果：行反正交矩阵是行列对称矩阵，它本身以及它的行转置和列转置矩阵都是可逆矩阵；行反正交矩阵的转置矩阵以及它的行转置和列转置矩阵都仍是行反正交矩阵；行反正交矩阵的行转置矩阵的逆矩阵等于其逆矩阵的行转置，其列转置矩阵的逆矩阵等于其逆矩阵的列转置；它的行转置矩阵的转置等于其转置矩阵的行转置，它的列转置矩阵的转置等于其转置矩阵的列转置。
給齣行反正交矩陣的概唸，併討論其行列式、可逆性、跡、特徵值等問題，得到行反正交矩陣的行列式、逆矩陣、特徵值與跡；併得齣瞭以下主要結果：行反正交矩陣是行列對稱矩陣，它本身以及它的行轉置和列轉置矩陣都是可逆矩陣；行反正交矩陣的轉置矩陣以及它的行轉置和列轉置矩陣都仍是行反正交矩陣；行反正交矩陣的行轉置矩陣的逆矩陣等于其逆矩陣的行轉置，其列轉置矩陣的逆矩陣等于其逆矩陣的列轉置；它的行轉置矩陣的轉置等于其轉置矩陣的行轉置，它的列轉置矩陣的轉置等于其轉置矩陣的列轉置。
급출행반정교구진적개념，병토론기행렬식、가역성、적、특정치등문제，득도행반정교구진적행렬식、역구진、특정치여적；병득출료이하주요결과：행반정교구진시행렬대칭구진，타본신이급타적행전치화렬전치구진도시가역구진；행반정교구진적전치구진이급타적행전치화렬전치구진도잉시행반정교구진；행반정교구진적행전치구진적역구진등우기역구진적행전치，기렬전치구진적역구진등우기역구진적렬전치；타적행전치구진적전치등우기전치구진적행전치，타적렬전치구진적전치등우기전치구진적렬전치。
This paper gives the concept of contrary orthogonal matrix, discusses determinant, reversibility, trace, eigenvalue and so on, and obtains determinant, inverse matrix, eigenvalue and trace of contrary orthogonalmatrix, meanwhile, draws the conclusion that contrary orthogonal matrix is a symmetric matrix of ranks, that itself, its row transposed matrix and its column transposed matrix are invertible, that the transposed matrix of contraryorthogonal matrix and its row transposed matrix and its column transposed matrix are also contrary orthogonal matrix, that inverse matrix of row transposed matrix of contrary orthogonal matrix is equal to its row transposition ofits inverse matrix, that the inverse matrix of its column transposed matrix is equal to its column transposition of its inverse matrix, that the transition of its row transposed matrix is equal to the row transposition of its transposedmatrix and that the transposition of its column transposed matrix is equal to the column transposition of its transposed matrix.
