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
Definition of orthogonal matrix
, where $R^T$ denotes the transpose of $R$, and $I$ denotes the identity matrix.
Example
  Show that the following matrix
An example of orthogonal matrix
is an orthogonal matrix.
Explanation
  By calculating concretely, we have
An example of orthogonal matrix
Therefore, $R$ is an orthogonal matrix.