Skew-Hermitian or Hermitian Matrix?

[jaus tail]

Homework Statement

Homework Equations

For Hermition: A = transpose of conjugate of A
For Skew Hermition A = minus of transpose of conjugate of A

The Attempt at a Solution

I think this answer is C. As Tranpose of conjugate of matrix is this matrix.
Book answer is D.
Am I wrong or is book wrong?

 

[Orodruin]

It is obviously Hermitian. It cannot be skew-hermitian. Skew-hermitian matrices cannot have real numbers on the diagonal as the diagonal elements need to satisfy $z^* = - z$.

 

[jaus tail]

Yeah. For skew hermitian, the diagonal elements are zero.

 

[Orodruin]

Yeah. For skew hermitian, the diagonal elements are zero.

This is not correct. The diagonal elements would be purely imaginary but not necessarily zero.

 

[StoneTemplePython]

Yeah. For skew hermitian, the diagonal elements are zero.

This holds if you are talking about real valued, skew symmetric matrices. But you aren't.
- - - -
the flip side is a Hermitian matrix must have entirely real components on its diagonal.

So Hermitian has purely real diagonal (possibly all zeros). Skew Hermitian has purely imaginary diagonal (possibly all zeros).

This should give you a hint at how these two matrices 'fit together'.