Given a square matrix A (say with complex entries), which is the sparsest matrix which is similar to A?

I guess it has to be its Jordan normal form but I am not sure.


  • A matrix is sparser than other if it has less nonzero entries.

  • Two square $n \times n$ matrices $A,C$ are similar if there exists and invertible matrix $P$ such that $A = P^{-1}CP$

  • 3
    $\begingroup$ Simulposted to (and answered at) m.se, math.stackexchange.com/questions/2961899/… $\endgroup$ – Gerry Myerson Oct 19 '18 at 12:00
  • 2
    $\begingroup$ Setting aside the cross-posting, the MSE answer shows that the guess is wrong but doesn't answer the question (which I assume is hard). $\endgroup$ – Ben Barber Oct 19 '18 at 13:58

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.