# 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 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.