安庆师范学院学报：自然科学版
安慶師範學院學報：自然科學版
안경사범학원학보：자연과학판
Journal of Anqing Teachers College(Natural Science Edition)
2011年
4期
97-100
,共4页
矩阵%正交矩阵%k-行正交矩阵%行列对称矩阵
矩陣%正交矩陣%k-行正交矩陣%行列對稱矩陣
구진%정교구진%k-행정교구진%행렬대칭구진
matrix%orthogonal matrix%K-row orthogonal matrix%row（column） symmetric matrix
给出k-行正交矩阵的概念,讨论其行列式、可逆性、迹、特征值等问题,得到k-行正交矩阵的行列式、逆矩阵、特征值与迹,得出了以下主要结果：k-行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;k-行正交矩阵的转置矩阵以及它的行转置和列转置矩阵仍都是k-行正交矩阵;k-行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k-行正交矩陣的概唸,討論其行列式、可逆性、跡、特徵值等問題,得到k-行正交矩陣的行列式、逆矩陣、特徵值與跡,得齣瞭以下主要結果：k-行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;k-行正交矩陣的轉置矩陣以及它的行轉置和列轉置矩陣仍都是k-行正交矩陣;k-行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。
급출k-행정교구진적개념,토론기행렬식、가역성、적、특정치등문제,득도k-행정교구진적행렬식、역구진、특정치여적,득출료이하주요결과：k-행정교구진시행렬대칭구진,타본신이급타적행전치화렬전치구진도시가역구진;k-행정교구진적전치구진이급타적행전치화렬전치구진잉도시k-행정교구진;k-행정교구진적행전치구진적역구진등우기역구진적행전치,기렬전치구진적역구진등우기역구진적렬전치;타적행전치구진적전치등우기전치구진적행전치,타적렬전치구진적전치등우기전치구진적렬전치。
We introduce the concept of K-row orthogonal matrix and discuss its determinant,reversibility,trace,elgenvalue problems.Then we obtain the following results that K-row orthogonal matrix is ranks of the symmetric matrix,which itself and its transpose rows and columns transposed matrix is invertible;all transpose matrix of K-row orthogonal matrix,and its transpose rows and columns transposed matrix are still k-row orthogonal matrix;K-row orthogonal matrix transpose matrix of rows is equal to the inverse matrix transpose,the columns transposed matrix of columns equal to the inverse matrix transpose;its row transpose a matrix is equal to the transposed matrix transpose row,its column transpose a matrix is equal to its transposed matrix transpose columns.
