一类特殊九对角对称正定矩阵特征值反问题
首发时间:2019-06-12
摘要:本文研究了一类特殊的九对角对称正定矩阵约束的线性矩阵方程的逆特征值问题,通过对矩阵的行列式计算, 得到矩阵行列式的通项公式, 在此基础上,确定矩阵的阶数为11时, 通过已知常数构造矩阵的特征值特征向量, 给出了此类方程有解的充分必要条件和解的表达式.
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Inverse Eigenvalue Problem for a Special Nine Diagonal Symmetric Positive Definite Matrix
Abstract:In this paper, the inverse eigenvalue problem of a special class of linear matrix equation constrained by nine diagonally symmetric positive definite matrices is studied. By calculating the determinant of the matrix, the general term formula of the matrix determinant is obtained. On this basis, when the order of the matrix is determined to be 11, the eigenvalue eigenvector of the matrix is constructed by known constants, and the necessary and sufficient conditions for the solution of the equation and the expression of the solution are given.
Keywords: determinant the linear matrix equation symmetric orthogonal matrix
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