%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 }