Solving for eigenvectors

06272016, 08:19 PM
Post: #1




Solving for eigenvectors
I would like if there is a fast method to find an eigenvector solving a matrix equation directly (knowing a given eigenvalue).
I work in CAS mode: If we have a matrix a=[[0,1,0,1,0],[0,0,0,0,0],[1,1,0,2,0],[1,3,0,0,0],[1,0,1,2,1]] We can check with the function "eigenvalue(a)" that 1 is an eigenvalue. Then if we put the following: (a*[[x1],[x2],[x3],[x4],[x5]]) = (1*[[x1],[x2],[x3],[x4],[x5]]) Is there any function that give us a vector like: [[1],[0],[3],[1],[1]] which fulfils the equation? The result that give the calculator is: [[(x2+x4) = (x1)],[0 = (x2)],[(x1+x2+2*x4) = (x3)],[(x1+3*x2) = (x4)],[(x1+x3+2*x4x5) = (x5)]] So I have to do many operations to obtain some vector from this. Is there some easy way to obtain a simple vector? Thanks in advance 

06282016, 07:29 AM
Post: #2




RE: Solving for eigenvectors
jordan
you can also do it by hand with ker(a(1)*identity(a)) 

06282016, 04:58 PM
Post: #3




RE: Solving for eigenvectors
Thank you very much.
Perfect, it works. 

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