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## Special Matrices

2013 | 1 | 1-2
Tytuł artykułu

### Nonnegative definite hermitian matrices with increasing principal minors

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A nonnegative definite hermitian m × m matrix A≠0 has increasing principal minors if det A[I] ≤ det A[J] for I⊂J, where det A[I] is the principal minor of A based on rows and columns in the set I ⊆ {1,...,m}. For m > 1 we show A has increasing principal minors if and only if A−1 exists and its diagonal entries are less or equal to 1.
Słowa kluczowe
EN
Wydawca
Czasopismo
Rocznik
Tom
Strony
1-2
Opis fizyczny
Daty
otrzymano
2013-08-06
zaakceptowano
2013-08-09
online
2013-10-02
Twórcy
autor
• Department of Mathematics, Statistics and Computer Science,
University of Illinois at Chicago, Chicago, Illinois 60607-7045, USA, friedlan@uic.edu
Bibliografia
• [1] D. Carlson, Weakly sign-symmetric matrices and some determinantal inequalities, Colloq. Math. 17 (1967), 123–129.
• [2] Ky Fan, Subadditive functions on a distributive lattice and an extension of Szász’s inequality, J. Math. Anal. Appl.18 (1967), 262–268.[Crossref]
• [3] Ky Fan, An inequality for subadditive functions on a distributive lattice, with application to determinantal inequalities,Linear Algebra Appl. 1 (1968), 33–38.[Crossref]
• [4] S. Friedland and S. Gaubert, Submodular spectral functions of principal submatrices of a hermitian matrix, extensionsand applications, Linear Algebra Appl., 438 (2013), 3872–3884.[WoS]
• [5] F. R. Gantmacher and M. G. Kre˘ın, Oszillationsmatrizen, Oszillationskerne und kleine Schwingungen mechanischerSysteme. Wissenschaftliche Bearbeitung der deutschen Ausgabe: Alfred Stöhr. Mathematische Lehrbücher undMonographien, I. Abteilung, Bd. V. Akademie-Verlag, Berlin, 1960.
• [6] S.A. Goreinov, E.E. Tyrtyshnikov, and N.L. Zamarashkin, A theory of pseudo-skeleton approximations of matrices,Linear Algebra Appl. 261 (1997), 1 – 21.
• [7] S. Iwata, Submodular function minimization, Math. Program. 112 (2008), 45–64.[WoS]
• [8] D. M. Kotelyanski˘ı, On the theory of nonnegative and oscillating matrices, Ukrain. Mat. Zh. 2 (1950), 94–101.
• [9] G. L. Nemhauser, L. A. Wolsey, and M. L. Fisher, An analysis of approximations for maximizing submodular setfunctions. I, Math. Program. 14 (1978), 265–294.[Crossref]
Typ dokumentu
Bibliografia
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