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Dominant Matrices

Zashmar

New member
Feb 24, 2013
5
Can anyone explain to a year 11 student what a dominant matrix is exactly?
my text book is not making much sense, i understand basic matricies and how you times them and rearange equations.

Thank you so much(Happy)
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Are you referring to diagonal dominance, and if so, is it row or column?
 

Zashmar

New member
Feb 24, 2013
5
Yes diagonally dominant, what does it mean
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Let's say it is row diagonal dominance.

For the $n$th row, the magnitude of the entry in the $n$th column must be greater than or equal to the sum of the magnitudes of all other entries in that row.

This must be true for all rows. Stated mathematically:

$\displaystyle |a_{ii}|\ge\sum_{j\ne1}|a_{ij}|$ for all $i$.

where $a_{ij}$ denotes the entry in the $i$th row and $j$th column.

Note that this definition uses a weak inequality, and is therefore sometimes called weak diagonal dominance. If a strict inequality (>) is used, this is called strict diagonal dominance. The unqualified term diagonal dominance can mean both strict and weak diagonal dominance, depending on the context.