|
|
back
|
Positive, Path Product, and Inverse M-matrices
|
An M-matrix is a square matrix with nonnegative off-diagonal M-matrices and a nonnegative inverse. The nonnegative
matrices that occur as inverses are called "inverse M-matrices" (IM for
short). Of course, not any nonnegative matrix is inverse M. We consider
the relations among entry-wise positive matrices, IM matrices and an
intermediate class, the path-product matrices. It is shown that any
positive matrix may be made path product via a sufficient addition to
its diagonal and any path product product matrix may be made IM via a
bounded addition to its diagonal. These results have implications for
questions about Hadamard products of IM matrices. |
back |
|
|