n维欧式空间中一个命题的证明

The Proof of a Proposition in Euclidean n-spaces

在n维欧式空间V中,V1,V2,…Vs-1是两两正交子空间,且dimV1+dimV2+…+dimVs-1=t<n。λ1,λ2,…λs-1,λs为s个互不相等的实数,则存在唯一的实对称矩阵A,使得λ1,λ2,…λs-1,λs为A的全部特征值且Vi为A的属于λi的特征子空间,其中i=1,2,…,s-1。本文给出了相关的证明。

in Euclidean n-spaces,V1,V2,…Vs-1 are orthogonal-each other subspace.dimV1+dimV2+…+dimVs-1=t<n.λ1,λ2,…λs-1,λs which aren't equal each other are real number.So there is the existence of unique real symmetric matrix A.λ1,λ2,…λs-1,λs are a full eigenvalue of real symmetric matrix A and Vi is A belong to λi 's feature subset spaces.This article gives the relevant evidence.