Hermitian matrix
From Conservapedia
A Hermitian matrix is one that satisfies 
, where 
is the Hermitian conjugate of 
(i.e., the matrix formed by transposing and taking the complex conjugate of each element). As an example, the most general 2x2 Hermitian matrix has the form
for any complex number 
and any real numbers 
and 
. In the case where all elements of the matrix are real, a Hermitian matrix becomes symmetric (as Hermitian conjugation then becomes equivalent to transposition).
Properties of Hermitian matrices
- The eigenvalues are all real.
- The eigenvectors corresponding to different eigenvalues are orthogonal.
Because of these properties, Hermitian matrices have important applications in quantum mechanics.
