MHB Understanding Dominant Matrices for Year 11 Students

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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)
 
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Are you referring to diagonal dominance, and if so, is it row or column?
 
Yes diagonally dominant, what does it mean
 
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.
 
The world of 2\times 2 complex matrices is very colorful. They form a Banach-algebra, they act on spinors, they contain the quaternions, SU(2), su(2), SL(2,\mathbb C), sl(2,\mathbb C). Furthermore, with the determinant as Euclidean or pseudo-Euclidean norm, isu(2) is a 3-dimensional Euclidean space, \mathbb RI\oplus isu(2) is a Minkowski space with signature (1,3), i\mathbb RI\oplus su(2) is a Minkowski space with signature (3,1), SU(2) is the double cover of SO(3), sl(2,\mathbb C) is the...

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