Nonnegative definite hermitian matrices with increasing principal minors

• Autorzy: Shmuel Friedland
• 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

Submodular functions; Hadamard-Fischer inequality; CUR approximations

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2013
• Tom: 1
• Strony: 1-2

Daty

otrzymano

2013-08-06

zaakceptowano

2013-08-09

online

2013-10-02

Twórcy

autor

Shmuel Friedland

• Department of Mathematics, Statistics and Computer Science,
  University of Illinois at Chicago, Chicago, Illinois 60607-7045, USA

Bibliografia

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Identyfikatory

DOI

10.2478/spma-2013-0001