Table of contents | |
---|---|

- | Definition |

- | Example |

- | Product |

- | Inverse |

- | Determinant |

Definition

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

Show that the following matrix
By calculating concretely, we have

Product

If $R$ and $S$ are orthogonal matrices,
then the product $RS$ are an orthogonal matrix as well.
It satisfies
Let $R$ and $S$ are orthogonal matrices. They satisfy

Inverse

The inverse matrix of an orthogonal matrix R is the transpose of $R$,
In general, the inverse matrix of a square matrix $A$ is a matrix $B$ that satisfies

Determinant

The determinant of an orthogonal matrix $R$ is $\pm 1$.
Let $R$ be an orthogonal matrix. We have