Normal matrices
From SklogWiki
A complex square matrix A is a normal matrix if
where 
is the conjugate transpose of A. That is, a matrix is normal if it commutes with its conjugate transpose: ![[A,A^\dagger]=0](/SklogWiki/images/math/b/2/e/b2ed6f9769d4ff25327d062ea7ce1614.png)
.
Normal matrices are precisely those to which the spectral theorem applies: a matrix A is normal if and only if it can be represented by a diagonal matrix Λ and a unitary matrix U by the formula
where
The entries λi of the diagonal matrix Λ are the eigenvalues of A, and the columns of U are the eigenvectors of A. The matching eigenvalues in Λ must be ordered as the eigenvectors are ordered as columns of U.
