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Form of symmetric matrix of rank one

  1. Apr 16, 2013 #1
    1. The problem statement, all variables and given/known data

    The question is:

    Let [itex]C[/itex] be a symmetric matrix of rank one. Prove that [itex]C[/itex] must have the form [itex]C=aww^T[/itex], where [itex]a[/itex] is a scalar and [itex]w[/itex] is a vector of norm one.

    2. Relevant equations

    3. The attempt at a solution
    I think we can easily prove that if [itex]C[/itex] has the form [itex]C=aww^T[/itex], then [itex]C[/itex] is symmetric and of rank one. But what about the opposite direction...that is what we need to prove. How to prove this?
  2. jcsd
  3. Apr 16, 2013 #2


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    Do you know that if C is symmetric, it can be diagonalized?
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