This is an attempt at a comprehensive expository study of those nonnegative matrices which happen to be inverses of M-matrices and is aimed at an audience conversant with basic ideas of matrix theory. A theme is the parallels (and differences) between the class of M-matrices and the class of inverse M-matrices. Among the primary tools used are diagonal multiplications, the Neumann expansion, and the form of the inverse of a partitioned matrix. Some of the results seem not to have appeared before, and several unsolved problems are mentioned.
%0 Journal Article
%1 johnson82
%A Johnson, Charles R.
%D 1982
%J Linear Algebra and its Applications
%K linear.algebra m-matrix
%P 195--216
%R 10.1016/0024-3795(82)90238-5
%T Inverse M-matrices
%V 47
%X This is an attempt at a comprehensive expository study of those nonnegative matrices which happen to be inverses of M-matrices and is aimed at an audience conversant with basic ideas of matrix theory. A theme is the parallels (and differences) between the class of M-matrices and the class of inverse M-matrices. Among the primary tools used are diagonal multiplications, the Neumann expansion, and the form of the inverse of a partitioned matrix. Some of the results seem not to have appeared before, and several unsolved problems are mentioned.
@article{johnson82,
abstract = {This is an attempt at a comprehensive expository study of those nonnegative matrices which happen to be inverses of M-matrices and is aimed at an audience conversant with basic ideas of matrix theory. A theme is the parallels (and differences) between the class of M-matrices and the class of inverse M-matrices. Among the primary tools used are diagonal multiplications, the Neumann expansion, and the form of the inverse of a partitioned matrix. Some of the results seem not to have appeared before, and several unsolved problems are mentioned.},
added-at = {2016-05-23T03:44:31.000+0200},
author = {Johnson, Charles R.},
biburl = {https://www.bibsonomy.org/bibtex/24a91bd41c294dde6db48cac45e7703b1/ytyoun},
doi = {10.1016/0024-3795(82)90238-5},
interhash = {13d63a6d6292e0b4fac31f8ca0dd1c46},
intrahash = {4a91bd41c294dde6db48cac45e7703b1},
issn = {0024-3795},
journal = {Linear Algebra and its Applications},
keywords = {linear.algebra m-matrix},
pages = {195--216},
timestamp = {2016-05-23T03:44:31.000+0200},
title = {Inverse {M}-matrices},
volume = 47,
year = 1982
}