摘要
本续文主要证明了如下结论:设A∈GL(n,R),矩阵A有对数主值lnA的充要条件是A没有负的特征值(定理2).并且,lnA是矩阵A的唯一对数的充要条件是A只有正的特征值,同时A无相同的初等因子(定理4).此外,还导出了矩阵A的对数LnA的通式(定理3).
In this successive paper, we prove mainly the folowing Theorem Let A∈GL(n,R). the matrix A has the principal value In A of its logarithm if and only if this A has no negative eigenvalues. Moreover, InA is the unique logarithm of A if and only if all eigenvalues of A are positive, and A has no same elementary divisors.
关键词
实矩阵
值
对数
矩阵
principal value, general expression of the matric logarithm
