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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

Groups audience:

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new question: Prove a formula is part of the Gentzen System by LadyAnne

Mar 30

new question: A problem about Euler's totient function by mbhatia

new problem: Problem: Show that phi(a^n-1), (where phi is the Euler totient function), is divisible by n for any natural number n and any natural number a >1. by mbhatia

new problem: MSC browser just displays "No articles found. Up to ." by jaimeglz

Mar 26

new correction: Misspelled name by DavidSteinsaltz

Mar 21

new correction: underline-typo by Filipe

Mar 19

new correction: cocycle pro cocyle by pahio

Mar 7

new image: plot W(t) = P(waiting time <= t) (2nd attempt) by robert_dodier

new image: expected waiting time by robert_dodier

new image: plot W(t) = P(waiting time <= t) by robert_dodier