## You are here

Homediagonally dominant matrix

## Primary tabs

# 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 $n$.

Defines:

strictly diagonally dominant matrix

Keywords:

Related:

Synonym:

diagonally dominant, strictly diagonally dominant

Type of Math Object:

Definition

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

15-00*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff
- Corrections