Spectral shorted matrices

Abstract

Given a n × n positive semidefinite matrix A and a subspace S of ℂn, ∑(S, A) denotes the shorted matrix of A to S. We consider the notion of spectral shorted matrix ρ(S, A) = limm→∞ ∑(S, Am)1/m. We completely characterize this martix in terms of script S sign 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 ℂn.