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

  1. 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?
  2. jcsd
  3. tiny-tim

    tiny-tim 26,016
    Science Advisor
    Homework Helper

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