# Finding eigen vectors of N-Dimensional linear transformation

1. Oct 20, 2011

### carlosgrahm

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