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Why the sum of cosines between "v`" and any vector =1?

  1. Feb 12, 2017 #1
    1. The problem statement, all variables and given/known data
    Given that matrix, A can be decomposed using SVD (Singular Value Decomposition) into ##A=USV^T##`, why does always the sum of the square of cosines between v` vectors and any other column vector q representation of arbitrarily column vector Q vector sum up to 1?

    2. Relevant equations
    ##A=USV^T##. ##Q=USq##

    3. The attempt at a solution
    I tried a simple 2x2 matrix but even with this simple matrix, the calculation goes missy. In addition, I seek a rigorous proof.
     
  2. jcsd
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