pyriemann.utils.base.powm

pyriemann.utils.base.powm(C, alpha)

Power of SPD/HPD matrices.

The symmetric matrix power \(\alpha\) of a SPD/HPD matrix \(\mathbf{C}\) is defined by:

\[\mathbf{D} = \mathbf{V} \left( \mathbf{\Lambda} \right)^{\alpha} \mathbf{V}^H\]

where \(\mathbf{\Lambda}\) is the diagonal matrix of eigenvalues and \(\mathbf{V}\) the eigenvectors of \(\mathbf{C}\).

Parameters:

Cndarray, shape (…, n, n)

SPD/HPD matrices, at least 2D ndarray.

alphafloat

The power to apply.

Returns:

Dndarray, shape (…, n, n)

Matrix power of C.