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  4. If A is a skew Hermitian matrix, then the main diagonal elements of A are all

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Q. If $A$ is a skew Hermitian matrix, then the main diagonal elements of $A$ are all

Matrices

Solution:

$A^*=-A=\Rightarrow(\bar{A})^{\prime}=-A \Rightarrow \overline{a_{i i}}=-a_{i i} \forall i $
$\Rightarrow 2 \operatorname{Re}\left(a_{i i}\right)=0 \Rightarrow a_{i i} \text { is purely imaginary. }$