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
Canonical name	FullyIndecomposableMatrix
Date of creation	2013-03-22 15:58:56
Last modified on	2013-03-22 15:58:56
Owner	Mathprof (13753)
Last modified by	Mathprof (13753)
Numerical id	10
Author	Mathprof (13753)
Entry type	Definition
Classification	msc 15A57
Defines	nearly decomposable
Defines	partly decomposable
Defines	fully indecomposable