Orthogonal matrix - properties and formulas -

	Table of contents
-	Definition
-	Example

Definition

Let $R$ be a square matrix. $R$ is called orthtonal matrix if it satisfies

, where $R^T$ denotes the transpose of $R$, and $I$ denotes the identity matrix.

Example

Show that the following matrix

Explanation
By calculating concretely, we have

Therefore, $R$ is an orthogonal matrix.