determining whether sets of matrices in a vectorspace are linearly independent?
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 semicolon 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? 
hi n00bot! :wink:
yes, that's correct :smile: … 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 :wink: 
Re: determining whether sets of matrices in a vectorspace are linearly independent?
OK, great! Thanks very much for the explanation :)

All times are GMT 5. The time now is 08:32 AM. 
Powered by vBulletin Copyright ©2000  2014, Jelsoft Enterprises Ltd.
© 2014 Physics Forums