About: Subtotally Positive and Monge Matrices     Goto   Sponge   NotDistinct   Permalink

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  • Reálná matice se nazývá k-subtotálně pozitivní, jsou-li determinanty všech jejích podmatic řádu nejvýše k kladné. Je ukázáno, že pro m x n matici stačí posoudit kladnost mn determinantů určitých podmatic k ověření k-subtotální pozitivity, a to pro každou volbu k, 1 <= k <= min(m, n). Jsou vyšetřeny spektrální vlastnosti čtvercových k-subtotálně pozitivních matic, studovány problémy doplnění 2-subtotálně pozitivních matic a jejich aditivních obdob, tzv. anti-Mongeových matic. Protože totálně pozitivní matice jsou i 2-subtotálně pozitivní, jsou tak získány nové nutné podmínky i pro totálně pozitivní matice. (cs)
  • A real matrix is called k-subtotally positive if the determinants of all its submatrices of order at most k are positive. We show that for an m x n matrix, only mn inequalities determine such class for every k, 1 <= k <= min(m, n). Spectral properties of square k-subtotally positive matrices are studied. Finally, completion problems for 2-subtotally positive matrices and their additive counterpart, the anti-Monge matrices, are investigated. Since totally positive matrices are 2-subtotally positive as well, the presented necessary conditions for this completion problem are also necessary conditions for totally positive matrices.
  • A real matrix is called k-subtotally positive if the determinants of all its submatrices of order at most k are positive. We show that for an m x n matrix, only mn inequalities determine such class for every k, 1 <= k <= min(m, n). Spectral properties of square k-subtotally positive matrices are studied. Finally, completion problems for 2-subtotally positive matrices and their additive counterpart, the anti-Monge matrices, are investigated. Since totally positive matrices are 2-subtotally positive as well, the presented necessary conditions for this completion problem are also necessary conditions for totally positive matrices. (en)
Title
  • Subtotally Positive and Monge Matrices
  • Subtotally Positive and Monge Matrices (en)
  • Subtotálně pozitivní a Mongeovy matice (cs)
skos:prefLabel
  • Subtotally Positive and Monge Matrices
  • Subtotally Positive and Monge Matrices (en)
  • Subtotálně pozitivní a Mongeovy matice (cs)
skos:notation
  • RIV/67985807:_____/06:00031791!RIV07-AV0-67985807
http://linked.open.../vavai/riv/strany
  • 177;188
http://linked.open...avai/riv/aktivita
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  • Z(AV0Z10300504)
http://linked.open...iv/cisloPeriodika
  • 2-3
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  • 502406
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  • RIV/67985807:_____/06:00031791
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  • totally positive matrix; Monge matrix (en)
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  • US - Spojené státy americké
http://linked.open...ontrolniKodProRIV
  • [4589A186B1C8]
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  • Linear Algebra and Its Applications
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  • 413
http://linked.open...iv/tvurceVysledku
  • Fiedler, Miroslav
http://linked.open...n/vavai/riv/zamer
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  • 0024-3795
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