Answer to Question #213089 in Linear Algebra for Dhruv bartwal

Question

If A is a hermitian matrix, then -A is skew-heritian.

True or false with full explanation

Answer 1

Given $A$ is Hermitian Matrix $\implies \bar{A}^T=A$

Now, Suppose $-A=B$ ;

$B=$ $-A=-{\bar{A}}^T=\bar {B}^T$ (Because $A$ is Hermitian Matrix )

$\implies$ $B=\bar {B}^T$

which means $B$ or $(-A)$ is Hermitian Matrix.

Hence If $A$ is a Hermitian matrix, then ' $-A$ is skew-Hermitian' is False.