Orthogonal matrix - properties and formulas -
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
is an
orthogonal matrix.
Explanation
By calculating concretely, we have
Therefore, $R$ is an orthogonal matrix.