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Finding eigen vectors of N-Dimensional linear transformation

  1. Oct 20, 2011 #1
    Definition of notation:
    First let x for this problem denote the elementart tensor product.
    Then let (AxB) acting on a vector v be defined by A<B,V> where this is the standard inner product.

    Problem statement
    With those defintions consider e and v members of Rn the vector space of N tuples allow A to be defined as A = exf +fxe
    find the
    eigen vectors
    eigen spaces
    specteral decompostition

    Relevent equations
    let the matrix that defines AxB be defined by (aibj) where ai and bj are the componets of the vectors

    Attempt at a soloution
    solve for Ag=g*lambda where we know g must be in the span{e,f}

    we know that there are only 2 non-zero eigen values because there are N-2 mutually orthogonal components to e and f.

    we can also know that all eigan values are real.

    Thanks for any help
  2. jcsd
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