An
matrix A is Hermitian if and only if it is normal and all of its eigenvalues are real.

Name: An matrix A is Hermitian if and only if it is normal and all of its eigenvalues are real.
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Question

An 
  matrix A is Hermitian if and only if it is normal and all of its eigenvalues are real.

Quizplus · Accepted Answer

A Hermitian matrix is a complex square matrix that is equal to its own conjugate transpose. It can also be shown that a matrix is normal if and only if it can be diagonalized by a unitary matrix, which means its eigenvalues are real. Therefore, a Hermitian matrix is both normal and has real eigenvalues.

An Matrix a Is Hermitian If and Only If