linear algebra question...

[Omegachi]

how do you express a 3x3 matrix as a product of elementary matrices?

 

[minendo]

4

 

[EvilYoda]

Don't quite remember, but I imagine that you use Gauss-Jordan reduction in some way. Or maybe Gaussian reduction. Don't you always do that?

From what I do remember, for a matrix to be a product of elementary matrices, it also means that it is invertible, so the RRE form is the identity matrix.

 

[bharok]

Originally posted by: Omegachi
how do you express a 3x3 matrix as a product of elementary matrices?

QR factorization ??
or
3x1 matrix times 1x3 matrix yeilds a 3x3 matrix

 

[His Lord Uberdude]

Originally posted by: minendo
4

Go away.

 

[her209]

Originally posted by: minendo
4

42

 

[Omegachi]

hmm... so i have to prove that it can inter change its i and j row col?

 

[SpecialEd]

please define elementary matrix

 

[EvilYoda]

an elementary matrix (E, E1, etc.) is just one that looks like: [1 0] or [0 1] or [0 0 1], etc.

 

[TuxDave]

How about a sum of products of elementry matrices and constants. :-D

 

[BRObedoza]

edit: nm i think i'm way off base

 

[wobbuffet]

Originally posted by: her209

Originally posted by: minendo
4

42

909

 

[Mo0o]

Originally posted by: wobbuffet

Originally posted by: her209

Originally posted by: minendo
4

42

909

The French Revolution!

 

[daniel1113]

I believe you need to find the eigenvalues (eigenvectors).

 

[bharok]

one example here
1________________________1 0 0
0 * [1 0 0 ] = IS A 3X3 MATRIX = { 0 0 0 }
0________________________0 0 0

Edit : tried to fix spacing

 

[MisterCornell]

I just had linear algebra my final semester of college (Spring 2004). I should know this one. Damn, my edumacation is slipping away from me

 

[bharok]

since u can make masic materices
using a linear combination of different elementary matrices u can make any matix