Proving a Hermitian matrix has real eigenvalues and orthogonal eigenspinors

[eman2009]

in the spin matrix if the <A> is real how we can prove the matrix is herimition ,and how we can prove the eigenvalues of any hermition 2x2 matrix is real and its eigenspinors are orthognal if the eigenvalues is defferent and if it is the same? and A physical quantity

 

[Meir Achuz]

Look in a math physics book.