Some interlacing theorems on the schur complement

Li, Chi-Kwong; Mathias, Roy

doi:10.1080/03081089808818572

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“…Many generalizations and applications came later. The reader is referred to the papers by Ando [3], Cottle [7], Carlson [6], Mitra [15], Butler and Morley [5], Pekarev [17], Pekarev and Smul'jan [18] and Li and Mathias [13,14] to have a complete panorama on these matters.…”

Section: Introductionmentioning

confidence: 99%

Spectral shorted matrices

Antezana

Corach

Stojanoff

2004

Linear Algebra and its Applications

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Given a n × n positive semidefinite matrix A and a subspace S of C n , R(S, A) denotes the shorted matrix of A to S. We consider the notion of spectral shorted matrix ρ(S, A) = lim m→∞ R(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 .

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