First slide

Transpose of matrix

Question

If $A = (\begin{array}{ccc} 2 & 3 - i & - i \\ 3 + i & π & 7 + i \\ i & 7 - i & e \end{array}),$ then $A$ is

Moderate

A

symmetric
B

Hermitian
C

skew Hermitian
D

none of these

Solution

We have
$\begin{array}{l} A^{'} = (\begin{array}{ccc} 2 & 3 + i & i \\ 3 - i & π & 7 - i \\ - i & 7 + i & e \end{array}) \\ \Rightarrow A^{*} = ({\bar{A}}^{'}) = (\begin{array}{ccc} 2 & 3 - i & - i \\ 3 + i & π & 7 - i \\ i & 7 + i & e \end{array}) = A \end{array}$
Thus $A$ is a Hermitian matrix.

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