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Homework Help: Advanced Linear Algebra Help

  1. Feb 10, 2014 #1
    1. The problem statement, all variables and given/known data
    Let T: C→D with dim(A)=n and dim(B)=m. Show that there exists bases B and B' for C and D, respectively, such that the matrix of T in block form is

    M=|I 0|
    |0 0|

    where I is a k by k identity matrix

    2. Relevant equations

    3. The attempt at a solution
    Honestly no idea where or how to start. Just looking for some hints and guided questions
  2. jcsd
  3. Feb 11, 2014 #2


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    Gold Member

    What is the purpose of the "dim(A)=n" statement.
    A is never used.
    Could you check the problem statement?
  4. Feb 11, 2014 #3
    Sorry for the mix up. It should be dim(C)=n and dim(D)=m
  5. Feb 11, 2014 #4
    So there exists {u1,u2,...,un} such that for any c that's an element of C we can make a linear combination of {u1,...un} that equals c. Similarly for {v1,v2,...vm} for any d that's an element of D
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