# Nonnegative definite hermitian matrices with increasing principal minors

Special Matrices (2013)

- Volume: 1, page 1-2
- ISSN: 2300-7451

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topShmuel Friedland. "Nonnegative definite hermitian matrices with increasing principal minors." Special Matrices 1 (2013): 1-2. <http://eudml.org/doc/267205>.

@article{ShmuelFriedland2013,

abstract = {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.},

author = {Shmuel Friedland},

journal = {Special Matrices},

keywords = {Submodular functions; Hadamard-Fischer inequality; CUR approximations; submodular functions},

language = {eng},

pages = {1-2},

title = {Nonnegative definite hermitian matrices with increasing principal minors},

url = {http://eudml.org/doc/267205},

volume = {1},

year = {2013},

}

TY - JOUR

AU - Shmuel Friedland

TI - Nonnegative definite hermitian matrices with increasing principal minors

JO - Special Matrices

PY - 2013

VL - 1

SP - 1

EP - 2

AB - 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.

LA - eng

KW - Submodular functions; Hadamard-Fischer inequality; CUR approximations; submodular functions

UR - http://eudml.org/doc/267205

ER -

## References

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