macierz ortogonalna

The product of two such matrices is a special orthogonal matrix which represents a rotation.

More generally, coordinate rotations in any dimension are represented by orthogonal matrices.

In this case, because and are real valued, they each are an orthogonal matrix.

The determinant of any orthogonal matrix is either +1 or 1.

Below are a few examples of small orthogonal matrices and possible interpretations.

A subtle technical problem afflicts some uses of orthogonal matrices.

Thus every rotation can be represented uniquely by an orthogonal matrix with unit determinant.

As it is an orthogonal matrix these diagonal elements are either 1 or 1.

Then, any orthogonal matrix is either a rotation or an improper rotation.

A general orthogonal matrix has only one real eigenvalue, either +1 or 1.