谱映像定理在欧氏空间中的另类证明

Another prove of spectrum mapping theory in Euclidean space

以泛函分析中的谱映像定量为基础,利用矩阵可以约化为若当型的特点,用一种非常简便的方法证明了欧氏空间中的谱映像定理,给出了一类矩阵指数特征值与原矩阵特征值之间的关系,并给出具体的实例验证结果的有效性.

Spectrum mapping theory in Euclidean space was proved with a simple method on the basis of the spectrum mapping theory in functional analysis by making use of the feature that a matrix can be reduced into Jordan. The relation was given between the eigenvalue of matrix exponent and the eigenvalue of the matrix, with an example cited to illustrate the effectiveness of the result.