# Symmetric Matrixes Thm

by blue_m
Tags: hermitian, matrices, skew, symmetric
 P: 341 For the first one, sufficiency is obvious. For necessity, either, write the explicit quadratic polynomial and plug in all values of x. Only possibility is the zero polynomial. Alternatively, Assume your $A=V\Lambda V^{-1}$ is diagonalizable with some Jordan blocks (possibly with size $k \times k$). And use the structure of the Jordan blocks.