Determining whether sets of matrices in a vectorspace are linearly independent?

[n00bot]

Given matrices in a vectorspace, how do you go about determining if they are independent or not?

Since elements in a given vectorspace (like matrices) are vector elements of the space, I think we'd solve this the same way as we've solved for vectors in R1 -- c1u1 + c2u2 + c3u3 = 0. But I'm not sure I'm setting it up right. I assume that three 2x2 matrices in r2, for example: (a,b;c,d), (e,f; g,h), (i,j;k,l) where a semi-colon denotes a new line, would be set up like this:

a e i
b f j
c g k
d h l

Am I understanding this correctly?

 

[tiny-tim]

hi n00bot!

yes, that's correct …

checking independence only involves scalar multiplication,

so the matrix structure is irrelevant, and you can treat the matrix components as if they were just vector components

 

[n00bot]

OK, great! Thanks very much for the explanation :)