Which of the following matrices are Hermitian? A = [2 3 - i 3 + i 4], B = [1 2i -2i 3 - i], C = [0 i i -i 0 i -i i 0]

Question

Which of the following matrices are Hermitian?

[latex]A = \left [ \begin{matrix} 2 & 3 - i \ 3 + i & 4 \end{matrix} ight ][/latex], [latex]B = \left [ \begin{matrix} 1 & 2i \ -2i & 3 - i \end{matrix} ight ][/latex], [latex]C = \left [ \begin{matrix} 0 & i & i \ -i & 0 & i \ -i & i & 0 \end{matrix} ight ][/latex]

Accepted Answer

We have [latex]A^∗ = \left [ \begin{matrix} 2 & 3 - i \ 3 + i & 4 \end{matrix} ight ] = A[/latex], so A is Hermitian.

[latex]B^∗ = \left [ \begin{matrix} 1 & 2i \ -2i & 3 + i \end{matrix} ight ] eq B[/latex], so B is not Hermitian.

[latex]C^∗ = \left [ \begin{matrix} 0 & i & i \ -i & 0 & -i \ -i & -i & 0 \end{matrix} ight ] eq C[/latex], so C is not Hermitian.

Question 9.5.1: Which of the following matrices are Hermitian? A = [2 3 - i ...

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