Recent content by spikedmath

  1. spikedmath

    Can we still diagnolize a matrix if its eigenvectors matrix is singular?

    If you don't have enough eigenvectors you can't diagonalize it. There is a theorem that says: An n-by-n matrix A is diagonalizable if and only if the sum of the dimensions of its eigenspaces is equal to n. However, you can 'almost' diagonalize any matrix you want. One way to do this is to use...
  2. spikedmath

    Can graph spectrums be derived from incident matrices?

    What is your definition for incident matrix? If it's the usual definition, then it's likely not a square (nxn) matrix so it doesn't make sense to talk about eigenvalues. You can however look at its singular values which I think are related to eigenvalues of the line graph of G.
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