My Math Forum Eigenvalue of matrix

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 February 4th, 2015, 12:19 PM #1 Senior Member   Joined: Feb 2015 From: london Posts: 121 Thanks: 0 Eigenvalue of matrix I have a matrix M, and I am trying to find the eigenvalues + eigenvector for this matrix $\displaystyle \left( \begin{array}{ccc} 1-x & x \\ y & 1-y \end{array} \right)$ 0 = det ( M - λI) 0 = λ^2 + λ(y + x -2) + 1 -x Not sure how to find the roots from here. The only other information I know is that x an y are between 0 and 1. But im not sure how that helps me. Any help if much appreciated. Last edited by calypso; February 4th, 2015 at 12:23 PM.
 February 4th, 2015, 12:56 PM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,344 Thanks: 2466 Math Focus: Mainly analysis and algebra Use the quadratic formula$$\lambda = \tfrac12 \left(2-x-y \pm \sqrt{ (y+x-2)^2 + 4(x-1) }\right)$$
 February 4th, 2015, 01:01 PM #3 Senior Member   Joined: Feb 2015 From: london Posts: 121 Thanks: 0 Thanks, yes I did try and use the quadratic formula. I got a similar answer to what you have posted. I suppose I expected the answer to produce 2 distinct roots. Maybe it doesnt and the furthest you go is to write what you have posted.
 February 4th, 2015, 02:16 PM #4 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,344 Thanks: 2466 Math Focus: Mainly analysis and algebra That is two roots. One where the $\pm$ is a plus, the other where it's a minus.

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