Compute the canonical form of an antisymmetric matrix.

The input is a real, antisymmetric n x n matrix A, where n is even. Its canonical form is::

A = R^T C R

where R is a real, orthogonal matrix and C has the form::

[  0     D ]
[ -D     0 ]

where D is a diagonal matrix with nonnegative entries.

antisymmetric_matrix ndarray

An antisymmetric matrix with even dimension.

canonical ndarray

The canonical form C of antisymmetric_matrix

orthogonal ndarray

The orthogonal transformation R.