Hermitian Matrix: Real & Imaginary Parts

[EngWiPy]

Hi,

Suppose that we have a complex matrix $$\mathbf{H}$$ that is Hermitian. The real part of the matrix will be symmetric, and the imaginary part of the matrix will be anti-symmetric. But what about the diagonal elements in the imaginary part? I mean we deduce that the elements in the diagonal of the imaginary part of the matrix equal the negative of themselves! What does this mean? or am I wrong?

Thanks in advance

 

[Petr Mugver]

y = - y implies y = 0 ... the diagonal elements of an hermitian matrix are real numbers.

 

[EngWiPy]

y = - y implies y = 0 ... the diagonal elements of an hermitian matrix are real numbers.

Are you saying that the diagonal elements of a Hermitian matrix are zero, or real and could be zero?

 

[uart]

Are you saying that the diagonal elements of a Hermitian matrix are zero, or real and could be zero?

He's saying that the imaginary part must be zero (for a number to be it's own conjugate). So yes he means real numbers not necessarily zero.

 

[EngWiPy]

He's saying that the imaginary part must be zero (for a number to be it's own conjugate). So yes he means real numbers not necessarily zero.

Ok, I got it. Thanks a lot.