First slide

Transpose of matrix

Question

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

Moderate

A

purely real
B

positive
C

negative
D

purely imaginary

Solution

$A^{â} = â A =â (\overset{Â¯}{A})^{â²} = â A â \overset{Â¯}{a_{i i}} = â a_{i i} â i$
$â 2 Re â¡ (a_{i i}) = 0 â a_{i i}$ is purely imaginary.

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