Question

线性空间2设V^(N*N),V1.V2分别为p上所有n级对称,反对称矩阵组成的子空间证明 v=V1+V2(直和的意思,加

Answer 1

1) V1+V2 included in V^(N,N) is trivial

2) To show the inverse inclusion,simply notice that for any A in V^(N,N),we have:

A = 1/2(A+A^T) + 1/2(A-A^T) with A^T transpose of A.

We conclude by noticing that (A+A^T) is symmetric and (A-A^T) is antisymmetric.