1. Not finding help here? Sign up for a free 30min 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!

Complex matrix space:

  1. Oct 3, 2007 #1
    1. The problem statement, all variables and given/known data
    If C is a n by n matrix with complex coefficient show that there is an integer k >0 that depends only on n such that C, C^2,C^3,...C^k are lin dependant.

    3. The attempt at a solution

    Its meant to be a full proof but the only idea I vaguely have is that i^4=i. I'm sure this is something standard to prove but I couldn't find it on google, so a link with an explanation would be appreciated.
     
  2. jcsd
  3. Oct 3, 2007 #2
    I can't remember much linear algebra but I would try considering the following. Suppose the dimension of a vector space is 6. Is it possible to extract 7 linearly independent vectors from that vector space?
     
  4. Oct 3, 2007 #3

    morphism

    User Avatar
    Science Advisor
    Homework Helper

    Cayley-Hamilton tells us that C satisfies its own characteristic polynomial.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?