Spectral shorted matrices

Abstract

Given a n x n positive semidefinite matrix A and a subspace S of C^n, Σ (S, A) denotes the shorted matrix of A to S. We consider the notion of spectral shorted matrix φ(S, A) = lim _{m→∞} Σ (S, A^m )^{1/m}. We completely characterize this martix in terms of S and the spectrum and the eigenspaces of A. We show the relation of this notion with the spectral order of matrices and the Kolmogorov´s complexity of A to a vector ξ ∈ C^n.