# fully indecomposable matrix

An $n\times n$ matrix $A$ that contains an $s\times(n-s)$ zero submatrix for some positive integer $s$ is said to be partly decomposable. If no such submatrix exists then $A$ is said to be it fully indecomposable. By convention, a $1\times 1$ matrix is fully indecomposable if it is nonzero. $A$ is nearly decomposable if it fully indecomposable but whenever a nonzero entry is changed to 0 the resulting matrix is partly decomposable.

Title fully indecomposable matrix FullyIndecomposableMatrix 2013-03-22 15:58:56 2013-03-22 15:58:56 Mathprof (13753) Mathprof (13753) 10 Mathprof (13753) Definition msc 15A57 nearly decomposable partly decomposable fully indecomposable