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

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SUMMARY

This discussion focuses on determining the linear independence of sets of matrices within a vector space. The method for assessing independence mirrors that used for vectors in R1, specifically through the equation c1u1 + c2u2 + c3u3 = 0. The participants confirm that the structure of the matrices is irrelevant, and their components can be treated as vector components for the purpose of checking independence.

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

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