关于可对角化线性算子的一点注记(英文)

The Note on Diagonalizable Linear Operators

域F上有限维向量空间V的线性算子τ∈L(V)可对角化当且仅当它的极小多项式mτ(x)是F上互异一次因式之积.文章将利用线性算子τ的特征值的初等对称多项式给出此结果的一个新证明.

A linear operator r∈ L（V） on a finite-dimensional vector space V is diagonalizable if and only if its minimal polynomial is the product of different linear factors. The paper gives a new proof for the result with elementary symmetric polynomials of its eigenvalues.