eigenvalues

Discussion in 'Math' started by braddy, Nov 2, 2005.

  1. braddy

    Thread Starter Well-Known Member

    Dec 29, 2004
    83
    0
    Hi, I need help for this problem:

    Find the eignevalues and eingenvectors for the matrix below. DO NOT compute them directly by computing the matrix:
    A-1


    We need to find some kind of demonstration to see if the eignevalues of A-1 are the same, opposite or inverse (or whatever) as those of matrix A
    Suppose that the eignvalues are 1,2,3 and the eignvectors are [1,1,0], [0,1,0],[ 3,-1,2] ( in columns)

    Does someone has any idea??
    Thank you
    B
     
  2. cookevillain

    New Member

    Dec 1, 2005
    4
    0
    Hi,

    I am afraid it is too late to answer this question as it was posted a month ago. But just in case.
    The eigenvectors will be the same but the eigenvalues will be the reciprocals of those for the original matrix (assuming A-1 is the inverse of A). It all follows from this simple computation:

    Ax = bx => A-1(Ax) = A-1bx => x = b A-1x => (1/b)x = A-1x (so x is an eigenvector of A with evalue 1/b)

    privided x is an eigenvector of A with eigenvalue b.
    Good luck.

    C-villain

     
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