pyriemann.utils.base.powm

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

Power of SPD matrices.

The matrix power \(\alpha\) of a SPD matrix C is defined by:

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

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

Parameters

Cndarray, shape (…, n, n)

SPD matrices, at least 2D ndarray.

alphafloat

The power to apply.

Returns

Dndarray, shape (…, n, n)

Matrix power of C.