Hermitian Matrix

Hermitian Matrix

Defintion 1. Let $A \in M_{n \times n}(F)$. We say that $A$ is hermitian (or self-adjoint) if $A = A^*$.

선형 연산자가 hermitian일 조건과 동일하게 hermitian인 행렬을 정의할 수 있다. 또한 Theorem 1의 행렬 버전을 말할 수 있다.

Theorem 1

Theorem 1. Let $A \in M_{n \times n}(\mathbb{R})$. Then $A$ is hermitian $\iff$ $A$ is orthogonally equivalent to a real diagonal matrix. 

Proof. The proof is similar to the proof of Theorem 1. $\blacksquare$