I'm working on this application where I get the spectral decomposition (O,D) of a matrix A for free (A is of full rank) but not A itself, and I need to only recover the last column of A. I was wondering if there was a more efficient way to do this than reconstructing the whole of A first?

  • 1
    $\begingroup$ What is $D$? Diagonal matrix of eigenvalues? Do you have the eigenvector matrices for free too? $\endgroup$ – Jesse Chan Mar 13 '14 at 17:53
  • $\begingroup$ @JLC: I edited the question to avoid confusion! Thanks for the hint $\endgroup$ – user189035 Mar 13 '14 at 19:05

Yes, for matrices A, B, the last column of matrix product A*B can be written as A*(the last column of B). You can use this fact to get the last column of the reconstruction using only O(N^2).

| cite | improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.