Class 28
-
Diagonalization of Hermitian Matrices
-
Lemma:
If A is Hermitian, then all eigenvalues are real.
-
Lemma:
If A is Hermitian, then eigenvectors corresponding to distinct
eigenvalues are orthogonal.
-
Definition:
The n by n matrix A is orthogonally (or unitary) diagonalizable if
A=PDP-1, where P is unitary, i.e. P*P=I
-
A is unitary diagonalizable iff A is Hermitian