Abstract: This specification relates to systems and methods for determining eigenvalues and eigenvectors of a covariance matrix, for example for use in eigen-beamforming in MIMO systems. According to a first aspect of this specification, there is describes a method comprising: receiving an input covariance matrix; and determining one or more eigenvalues and/or eigenvectors of the matrix iteratively using gradient ascent, wherein each iteration of the gradient ascent has a step size, ?, that maximises a Rayleigh quotient along the gradient.