Answer to Question #213089 in Linear Algebra for Dhruv bartwal

Question #213089

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

True or false with full explanation


1
Expert's answer
2021-07-05T17:31:23-0400

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

Now, Suppose A=B-A=B ;

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

    \implies B=BˉTB=\bar {B}^T

which means BB or (A)(-A) is Hermitian Matrix.

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




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