Find the eigenvalues and eigenvectors for the matrix

  • #1

Homework Statement


Find the eigenvalues and eigenvectors for the matrix [{13,5},{2,4}]

Homework Equations


None

The Attempt at a Solution


Well eigenvalues is easy, and turn out to be 14 and 3.
So using eigenvalue 3, the two equations 10x1 + 5x2=0 and 2x1 + x2=0. Using these, I assumed the eigenvector to be [1,-2] but after putting it into Wolfram (or mathematica) it gives out the vector should be [-1,2]. Is there a difference? How should you discern between the two if not and where have I gone wrong if there is?
 

Answers and Replies

  • #2
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Homework Statement


Find the eigenvalues and eigenvectors for the matrix [{13,5},{2,4}]

Homework Equations


None

The Attempt at a Solution


Well eigenvalues is easy, and turn out to be 14 and 3.
So using eigenvalue 3, the two equations 10x1 + 5x2=0 and 2x1 + x2=0. Using these, I assumed the eigenvector to be [1,-2] but after putting it into Wolfram (or mathematica) it gives out the vector should be [-1,2]. Is there a difference? How should you discern between the two if not and where have I gone wrong if there is?
Assuming your work is correct, there is no difference between <1, -2> and <-1, 2> as far as being eigenvectors. Each of these vectors is the -1 multiple of the other, so they are both in the same eigenspace, a subspace of dimension 1 (a line) in R2.
 
  • #3


Great. So do programs like mathematica choose them at random or is there a reason it chose <-1,2> over <1,-2>?
 
  • #5


Ok, thanks for the help!
 

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