K-行正交矩阵的一些性质

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。

Some Properties of the K-Row Orthogonal Matrices

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.