Abstract: This paper generalizes the corresponding results in[2], Some upper bounds of the matrix Rayleigh quotient X'AX(X'X)^-1 and general form X'AX(X'BX)^-1 are given with the measures of trace, spectral norm and Euclidean norm. Here A and B are all nXn positive definite matrixes. X is nxp matrix of ranks p.

Key words: Rayleigh quotient, norm, conditional number, Poincare theorem

摘要： 本文推广了文献[2]中相应的结果,给出了一般的矩阵Rayleigh商X'AX(X'X)^-1及其一般形式X'AX(X'BX)^-1在矩阵迹,谱范数和欧氏范数三种度量下的上界。这里A、B为n阶正定阵,X为n×p列满秩矩阵。

关键词: Rayleigh商, 范数, 条件数, Poincaré, 定理