A positive semidefinite (PSD) operator A "spectrally dominates" a PSD operator B if At - Bt is PSD for all t> 0. We (i) give a new characterization of spectral dominance in finite dimensions in terms of a monotonic chain of intermediate, pairwise commuting operators and (ii) determine for which pairs A, B spectral dominance persists under the taking of arbitrary compressions. Earlier results about spectral dominance are proven (in finite dimensions) in new ways, and several corollary observations are made.
ASJC Scopus subject areas
- Applied Mathematics