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Math Help - Eigenvectors under scaling/ matrix approximation

  1. #1
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    Eigenvectors under scaling/ matrix approximation

    * corresponds to matrix product
    I'm working on a method of visualising graphs, and that method uses eigenvector computations. For a certain square matrix K (the entries of which are result of C_transpose*C, therefore K is symmetric) I have to compute the eigenvectors.
    Since C is mXn, where m>>n, I go with a portion of C (NOT the dot product of the COMPLETE first row of C_transpose with the complete first column of C, but the portion (1/5 perhaps), meaning the dot product of the PORTION of the first row of C_transpose with the portion of the first column of C). In order to get good approximation of the original COMPLETE C_transpose*C, I'm not sure whether I need to multiply each entry of K with 5 (see 1/5 above).
    How would the eigenvectors behave if I do not perform the multiplication with 5?

    In addition, any other suggestion how to approximate C_transpose*C, where C is mXn matrix, with m>>n are very welcome.
    I hope I explained the problem properly.
    Thanks
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  2. #2
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    The answer for this: entries of a real symmetric matrix are scaled, the eigenvalues are scaled, but the eigenvectors stay same.
    However, I would really be happy to consider your opinion on this:
    any other suggestion how to approximate C_transpose*C, where C is mXn matrix, with m>>n are very welcome.
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