Geodesic
Products of $M$-matrices and nested sequences of principal minors
The electronic journal of linear algebra, Tome 16 (2007), pp. 380-388.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The question of whether or not the product of two nonsingular n-by-n M-matrices has a nested sequence of positive principal minors (abbreviated to a nest) is considered. For n = 2, 3, 4 such a product always has a nest, and this is conjectured for n = 5. For general n, examples of products of two M-matrices with specified structure are identified as having a leading or trailing nest. For n = 4, it is shown that the cube of an M-matrix need not have a nest.
Classification : 15A15
Keywords: M-matrix, nested sequence of principal minors, P -matrix 
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     title = {Products of $M$-matrices and nested sequences of principal minors},
     journal = {The electronic journal of linear algebra},
     pages = {380--388},
     publisher = {mathdoc},
     volume = {16},
     year = {2007},
     language = {en},
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Grundy, D.A.; Johnson, C.R.; Olesky, D.D.; van den Driessche, P. Products of $M$-matrices and nested sequences of principal minors. The electronic journal of linear algebra, Tome 16 (2007), pp. 380-388. http://geodesic.mathdoc.fr/item/ELA_2007__16__a6/