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Column subspace problem

  1. Oct 29, 2009 #1
    Let A_i (i=1,...,k) be a nonsingular complex matrix which size is M by M.
    The question is how to find a complex matrix X which size is M by N such that:

    span(A_1*X)=...=span(A_k*X)

    (I guess that there must be relations between M,N and k when nontrival solution exists. )
    ask:
    1)if non trival solwhat's the condition for the existence of nontrival solutions?
    2)Is there any method or related references for this question?

    Thanks in advance:)
     
  2. jcsd
  3. Oct 31, 2009 #2

    HallsofIvy

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    It seems to me that a rather obvious thing to do is to add N-M rows that are just multiples, or linear combinations, of the original rows.
     
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