MHB Understanding Dominant Matrices for Year 11 Students

[Zashmar]

Can anyone explain to a year 11 student what a dominant matrix is exactly?
my textbook is not making much sense, i understand basic matricies and how you times them and rearange equations.

Thank you so much(Happy)

 

[MarkFL]

Are you referring to diagonal dominance, and if so, is it row or column?

 

[Zashmar]

Yes diagonally dominant, what does it mean

 

[MarkFL]

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.