伴随表示下矩阵的谱

Spectrum of Matrix's Accompanying Representation

首先证明了若矩阵相似,矩阵的伴随表示也相似.通过计算若当矩阵的伴随表示在一组标准基下的作用,揭示了矩阵的谱和其伴随表示的谱之间的关系,并给出了具体的表达式.

At first, the fact is proved to be right that if the matrices are similar, their adjoint representations are similar too. By computing Jordan matrix＇s adjoint representation acting on a normal base, we show the relationship between the spectrum of matrix and the spectrum of adjoint representation, and give out the specific formula.