Geodesic
Path product and inverse M-matrices
The electronic journal of linear algebra, Tome 22 (2011), pp. 644-652.

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

Summary: It is known that inverse M-matrices are strict path product (SPP) matrices, and that the converse is not true for matrices of order greater than 3. In this paper, given a normalized SPP-matrix A, some new values s $^{\prime}$ for which A + s $^{\prime}$ Iis an inverse M-matrix are obtained. Our values s $^{\prime}$ extend the values s given by Johnson and Smith [C.R. Johnson and R.L. Smith. Positive, path product, and inverse M-matrices. Linear Algebra Appl., 421:328-337, 2007.]. The question whether or not a $4 \times 4$ SPP-matrix is a P-matrix is settled.
Classification : 15A48, 15A57
Keywords: M-matrix, inverse M-matrix, path product matrix, P-matrix 
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     author = {Zhu, Yan and Zhang, Cheng-Yi and Liu, Jun},
     title = {Path product and inverse {M-matrices}},
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Zhu, Yan; Zhang, Cheng-Yi; Liu, Jun. Path product and inverse M-matrices. The electronic journal of linear algebra, Tome 22 (2011), pp. 644-652. http://geodesic.mathdoc.fr/item/ELA_2011__22__a35/