Orthogonal Matrix

Definition

A matrix is orthogonal if the Matrix Transposition is the Inverse Matrix, then that transposition is orthogonal. Conventionally, the orthogonal matrix is used for Real Number

Formal Definition

A matrix $A\in {\mathbb{R}}^n$ is Orthogonal Matrix if $A{A}^T=A^{T}A=I_n$

(Or $A^T=A^{-1}⟺A\text{ is orthoganal}$)

Theorems

• Orthogonal and Determinant Theorem