diagonally dominant matrix

Let $A$ be a square matrix of order $n$ with entries $a_{ij}$ which are real or complex. Then $A$ is said to be diagonally dominant if

$$|a_{ii}|\ge \sum _{j=1,j\ne i}^n|a_{ij}|$$

for $i$ from $1$ to $n$.
In addition $A$ is said to be strictly diagonally dominant if

$$|a_{ii}|>\sum _{j=1,j\ne i}^n|a_{ij}|$$

for $i$ from $1$ to $n$.

Title	diagonally dominant matrix
Canonical name	DiagonallyDominantMatrix
Date of creation	2013-03-22 13:47:46
Last modified on	2013-03-22 13:47:46
Owner	Daume (40)
Last modified by	Daume (40)
Numerical id	7
Author	Daume (40)
Entry type	Definition
Classification	msc 15-00
Synonym	diagonally dominant
Synonym	strictly diagonally dominant
Defines	strictly diagonally dominant matrix