Multiplicative perturbation bounds for multivariate multiple linear regression in Schatten p-norms

Multivariate multiple linear regression (MMLR), which occurs in a number of practical applications, generalizes traditional least squares (multivariate regression) to right-hand sides. We extend recent MLR analyses sketched MMLR general Schatten p-norms by interpreting the problem as multiplicative perturbation. Our work represents an extension Maher's results on p-norms. derive expressions for exact and perturbed solutions terms projectors easy geometric interpretation. also present interpretation action sketching matrix relevant subspaces. show that key term assessing accuracy solution can be viewed tangent largest principal angle between subspaces under some assumptions. enable additional difference orthogonal oblique projector with same range.