# 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

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

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

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

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

Title diagonally dominant matrix DiagonallyDominantMatrix 2013-03-22 13:47:46 2013-03-22 13:47:46 Daume (40) Daume (40) 7 Daume (40) Definition msc 15-00 diagonally dominant strictly diagonally dominant strictly diagonally dominant matrix