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A conjecture concerning the Hadamard product of inverses of M-matrices

โœ Scribed by M. Neumann

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
804 KB
Volume
285
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

We conjecture that for an n x n matrix A which is an inverse of an M-matrix, the Hadamard product A o A is also an inverse of an M-matrix. We have checked this conjecture without failure on many many examples. But here we show that for quite a few well known classes of inverses of M-matrices, the conjecture is true. It is known that the more general conjecture, that when A and B are n x n inverses of M-matrices, then A o B is also an inverse of an M-matrix, is false. However, here too we are able to display some classes of inverses of M-matrices which are closed under taking Hadamard products.

๐Ÿ“œ SIMILAR VOLUMES

On the Hadamard product of inverse M-mat
On the Hadamard product of inverse M-matrices
โœ Bo-Ying Wang; Xiuping Zhang; Fuzhen Zhang ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 79 KB

We investigate the Hadamard product of inverse M-matrices and present two classes of inverse M-matrices that are closed under the Hadamard multiplication. In the end, we give some inequalities on the Fan product of M-matrices and Schur complements.