def geodesic_euclid(A, B, alpha=0.5):
    """Return the matrix at the position alpha on the euclidean geodesic between A and B  :

    .. math::
            \\mathbf{C} = (1-\\alpha) \\mathbf{A} + \\alpha \\mathbf{B}

    C is equal to A if alpha = 0 and B if alpha = 1

    :param A: the first coavriance matrix
    :param B: the second coavriance matrix
    :param alpha: the position on the geodesic
    :returns: the covariance matrix

    """
    return (1 - alpha) * A + alpha * B
