This paper continues the early studies on eigenvalue perturbation theory for diagonalizable matrix pencils having real spectral (Math. A unifying framework of creating crucial perturbation equations are developed. With the help of a recent result on generalized commutators involving unitary matrices, new and much sharper bounds are obtained. Abstract This paper continues the early studies on ei...

We presented a new lower bound on minimal singular values of real matrices based on Frobenius norm and determinant and showed in [4] that under certain assumptions on the matrix is our estimate sharper than a recent lower bound from Hong and Pan [3]. In this paper we show, under which conditions is our lower bound sharper than two other recent lower bounds for minimal singular values based on a...

We prove a result about the action of λ-operations on the homology of linear groups. We use this to give a sharper formulation of the rank conjecture as well as some shorter proofs of various known results. We formulate a conjecture about how the sharper formulation of the rank conjecture together with another conjecture could give rise to a different point of view on the isomorphism between CH...