
Linear Algebra Linear Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
October 30th, 2012, 11:14 AM  #1 
Newbie Joined: Oct 2012 Posts: 15 Thanks: 0  Eigenvector of symmetric matrix
the vector (1 0 1)^t is an eigenvector of the symmetric matrix 6 1 3 1 7 x 3 x y how can i find x and y and the corresponding eigenvalue l.. I have no idea how to approach this question.. my understanding is that (1 0 1)^T is actually: 1 0 1 rows become columns and all that.. but how i can find the eigenvalue and original vector using this i dont know.. any help is appreciated! 
November 6th, 2012, 06:09 AM  #2 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Eigenvector of symmetric matrix
Do you not know what "eigenvalue" and "eigenvector" mean? A vector, v, is an eigenvector of linear transformation A, with eigenvalue , if and only if . I don't know what you mean by "the original vector". The is only one vector and it is given. Since we are told that is an eigenvector there must be a number such that . Multiplying out that left side, which gives the three equations , , and . That's pretty easy, isn't it? 

Tags 
eigenvector, matrix, symmetric 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Eigenvector of 3x3 matrix  jones123  Calculus  2  May 30th, 2013 07:51 AM 
symmetric matrix and eigenvalues  buttnana  Linear Algebra  1  September 26th, 2011 12:55 PM 
Urgent Eigenvector decomposition of a matrix  Sergio  Economics  0  June 6th, 2010 02:03 AM 
Symmetric matrix and eugenvalues..  BlackOps  Linear Algebra  2  February 18th, 2010 08:01 AM 
Positive Real Matrix Eigenvector  skeboy  Linear Algebra  0  June 11th, 2009 10:51 PM 