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Homediagonally dominant matrix

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# 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

Synonym:

diagonally dominant, strictly diagonally dominant

Type of Math Object:

Definition

Major Section:

Reference

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