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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