Nonnegative definite hermitian matrices with increasing principal minors
Shmuel Friedland
Special Matrices, Tome 1 (2013), p. 1-2 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2013-01-01
EUDML-ID : urn:eudml:doc:267205 
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     author = {Shmuel Friedland},
     title = {Nonnegative definite hermitian matrices with increasing principal minors},
     journal = {Special Matrices},
     volume = {1},
     year = {2013},
     pages = {1-2},
     zbl = {1291.15089},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_spma-2013-0001}
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Shmuel Friedland. Nonnegative definite hermitian matrices with increasing principal minors. Special Matrices, Tome 1 (2013) pp. 1-2. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_spma-2013-0001/

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