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Showing a set of matrices is a group

by bennyska
Tags: matrices, showing
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Feb12-10, 10:31 PM
P: 111
1. The problem statement, all variables and given/known data
show the set of nxn diagonal matrices is a group under matrix addition

2. Relevant equations

3. The attempt at a solution
it doesn't say what set the entries are from, so i'm assuming it's reals.
so i need to show that there is closure, it's associative, there's an identity element, and there's an inverse. i know that there's an identity element, the matrix with just zeroes, and i know the inverse is just -A for matrix A. it's addition, so i know that it's associative, and in my head i can tell that there is closure.
my main problem is notation. how to do i actually express this? i.e., what's the general notation for a nxn matrix?
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Feb13-10, 01:08 AM
P: 211
Here is a general diagonal nxn matrix:

[tex]\left( \begin{array}{c c c c} x_1 & & & \\ & x_2 & & \\ & & ... & \\ & & & x_n \end{array} \right)[/tex]

Alternatively, you can say "let A be a diagonal nxn matrix" and index the entries with [itex]A_{ij}[/itex].

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