矩阵的次特征值及其应用

The subeigenvalue of matrix and its applications

矩阵的次特征值、次特征向量和次相似变换概念分别是特征值、特征向量和相似变换概念的自然延伸,它们同样具有明显的几何意义以及几何应用.证明了矩阵的次特征值是次相似变换下的全系不变量.利用次正定矩阵的性质,建立了次正定矩阵的一个基本不等式.同时给出了实对称矩阵次特征值的变分特征.

The subeigenvalue, subelgenvector and subsimilarity transformation of matrix are the extension of eigenvalue, elgenvector and similarity transformation, respectively, and have geometric significance and extensive applications, especially in distance geometry. It was proved that the subeigenvalue of a matrix is the complete system of invariant for the subsimilar transformation. Using the property of subpositive definite matrices, a basic inequality about subpositive definite matrices was established. At the same time, the variational characterizations of a real symmetric matrix were given.