Loading...
Please wait, while we are loading the content...
Similar Documents
The Moore-Penrose inverse of matrices with an acyclic bipartite graph (2004)
| Content Provider | CiteSeerX |
|---|---|
| Author | Britz, T. Olesky, D. D. Driessche, P. Van Den |
| Abstract | The Moore-Penrose inverse of a real matrix having no square submatrix with two or more diagonals is described in terms of bipartite graphs. For such a matrix, the sign of every entry of the Moore-Penrose inverse is shown to be determined uniquely by the signs of the matrix entries; i.e., the matrix has a signed generalized inverse. Necessary and sufficient conditions on an acyclic bipartite graph are given so that each nonnegative matrix with this graph has a nonnegative Moore-Penrose inverse. Nearly reducible matrices are proved to contain no square submatrix having two or more diagonals, implying that a nearly reducible matrix has a signed generalized inverse. Furthermore, it is proved that the term rank and rank are equal for each submatrix of a nearly reducible matrix. |
| File Format | |
| Publisher Date | 2004-01-01 |
| Access Restriction | Open |
| Subject Keyword | Moore-penrose Inverse Acyclic Bipartite Graph Reducible Matrix Generalized Inverse Real Matrix Matrix Entry Square Submatrix Bipartite Graph Term Rank Nonnegative Matrix Nonnegative Moore-penrose Inverse |
| Content Type | Text |
