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Vector transformations that lead to the identity matrix

  1. Nov 25, 2012 #1
    Hi all,

    I have a question that seems very simple but I just do not see it;)

    Let α denote an r×1 vector with arbitrary entries; I'm trying to construct an 1×r vector m such that αm = I, where I is the r×r identity matrix...

    The first question is: is this possible?

    I tried the following;

    let m = α'(α α')^{-1}, but then the problem is that (α α')^{-1} is not defined (rank 1)
    how can I fix this;

    Thanks in advance Geert
  2. jcsd
  3. Nov 25, 2012 #2


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    You can't. For any two vectors α and m, αm has rank 1. I has rank r.
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