My Math Forum  

Go Back   My Math Forum > College Math Forum > Linear Algebra

Linear Algebra Linear Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
February 4th, 2015, 01:19 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 01:23 PM.
calypso is offline  
 
February 4th, 2015, 01:56 PM   #2
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,031
Thanks: 2342

Math Focus: Mainly analysis and algebra
Use the quadratic formula$$\lambda = \tfrac12 \left(2-x-y \pm \sqrt{ (y+x-2)^2 + 4(x-1) }\right)$$
v8archie is offline  
February 4th, 2015, 02:01 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.
calypso is offline  
February 4th, 2015, 03:16 PM   #4
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,031
Thanks: 2342

Math Focus: Mainly analysis and algebra
That is two roots. One where the $\pm$ is a plus, the other where it's a minus.
v8archie is offline  
Reply

  My Math Forum > College Math Forum > Linear Algebra

Tags
eigenvalue, matrix



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Eigenvalue Problem subhajit028 Linear Algebra 3 September 16th, 2013 01:00 PM
how to get the eigenvector and the corresponding eigenvalue lakayii Linear Algebra 2 September 24th, 2012 08:48 AM
Eigenvalue wannabe1 Linear Algebra 2 April 17th, 2010 03:33 PM
eigenvalue tinynerdi Linear Algebra 3 April 5th, 2010 01:56 AM
how to get the eigenvector and the corresponding eigenvalue lakayii Algebra 1 December 31st, 1969 04:00 PM





Copyright © 2017 My Math Forum. All rights reserved.