1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Trivial question!

  1. Nov 5, 2006 #1
    Can a zero matrix be considered as nilpotent matrix?
    Zero matrix raised to any positive power is zero matrix, so can it be considered nilpotent (with index of nilpotency being 1)? I have read the definition of the nilpotent matrix and it doesn't that say that a matrix has to different from 0, but I'm still confused...
  2. jcsd
  3. Nov 5, 2006 #2
    sure, you can say that the zero matrix is nilpotent, but that would be considered the trivial case. i.e., if you are asked to find a nilpotent matrix satisfying some properties, using the zero matrix will probably not get you credit for solving the question.
  4. Nov 6, 2006 #3


    User Avatar
    Science Advisor

    Why are you confused? Another characterization of "nilpotent" is that a matrix is nilpotent if and only if its eigenvalues are all 0. That is certainly true of the 0 matrix. The 0 matrix is definitely nilpotent.
  5. Nov 8, 2006 #4
    Thank you!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook