Question

A是对称矩阵,B可以由A的多项式矩阵表示,那么B一定为对称矩阵吗?

Answer 1

是的

B^T=(A^5-4A^3+E)^T=(A^5)^T-(4A^3)^T+E

=(A^T)^5-4(A^T)^3+E

=A^5-4A^3+E

=B

B为对称矩阵