[LA] Normal Matrix (정규행렬)

Normal Matrix란?

Matrix $A \in M_n (C)$에 대해 (◀ Matrix가 Complex Number를 가질 수 있으며, $n\times n$ Square Matrix임),
다음을 만족하면 $A$를 Normal Matrix (정규행렬)이라고 부름.
$$A{A^*}^\top(=AA^H)={A^*}^\top A(=A^H A)$$

where

• $A^\top$ : Transpose of $A$ (전치)
• $A^H$ : $A$의 각 entity에 complex conjugate 를 취하고 Transpose한 것. Herimitian Adjoint 라고도 부름.
• $A^*$ : $A$의 각 entity에 complex conjugate 취한 행렬. 

Normal matrix의 가장 큰 특징 중 하나는 항상 Diagonlizable이라는 점임.

• Symmetric matrix 와 Hermitian matrix가 Normal matrix에 속함! 

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참고자료

2022.11.17 - [.../Linear Algebra] - [LA] Diagonalization (Eigen-Decomposition), Orthogonal Diagonalization, and Symmetric Matrix

[LA] Diagonalization (Eigen-Decomposition), Orthogonal Diagonalization, and Symmetric Matrix

2022.11.25 - [.../Math] - [LA] Hermitian Matrix and Unitary Matrix

[LA] Hermitian Matrix and Unitary Matrix

 

https://bme808.blogspot.com/2022/11/math-hermitian-symmetry.html

Math : Hermitian Symmetry

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