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Eigenvectors pr0blem!

  • 20-04-2006 4:15pm
    #1
    [Deleted User]
    Posts: 8,647 ✭


    Hi!Im doing first year maths in NUIG!Im freaking because i cant do the last part of my eigenvectors questions.Its asks me to find A^100 after finding AE=ED d=diagonal matrix and E=invertible matrix(which i can do).It has me all confused and its coming up in my exam tomorrow.I've looked for answers through google but that only gives me theory which makes me more confused.

    Any help would be much appreciated!


Comments

  • #2
    whyamihere?
    Closed Accounts Posts: 26 ✭whyamihere?


    you have AE=ED therefore A=EDE^(-1) (where E^(-1)=inverse of E)
    therefore A^100=EDE^(-1)EDE^(-1)ED...a hundred times
    but E^(-1)E=1
    therefore A^100=ED^100E^(-1)
    which is easy to compute considering D is diagonal


  • #3
    [Deleted User]
    Posts: 8,647 ✭ [Deleted User]


    so you mean e^-1 x e^1 gives you one?


  • #4
    Michael Collins
    Moderators, Science, Health & Environment Moderators Posts: 1,851 Mod ✭✭✭✭Michael Collins


    Deleted User wrote:
    so you mean e^-1 x e^1 gives you one?

    Well not quite, it gives you the identity matrix, which is ones on the diagonal and zeros everywhere else - which just gives you back whatever matrix is multipled by it or that it is multiplied by...


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