Example 5: A Hermitian matrix
A = 2 1+j 2-j,
1-j 1 j
2+j -j 1
= 2 1-j 2+j  (j2 = -1)
1+j 1 -j
2-j j 1
Now AT = => A is Hermitian (the ij-element is conjugate to the ji-element). Since A is Hermitian, we have AH = A = T. The diagonal elements of a Hermitian matrix are real.
A = j 1-2j,
-1-2j 0
= -j 1+2j,
-1+2j 0
- = j -1-2j = BT
1-2j 0
=> B is skew Hermitian (a skew Hermite matrix). The diagonal elements of a skew Hermitian matrix are pure imaginary or zero.

For vectors we have

= x1    , T = (x1 x2 x3 ) = (x1 , x2 , x3 )
x2
x3
= (y1 , y2 , y3 ),    T = y1 .
y2
y3
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