- #1
asif zaidi
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Homework Statement
My problem is I am getting a different answer than what MATLAB is giving me and I cannot determine why. Plz advise.
Find an orthonormal basis of eigenvectors for matrix A= [3 2; 2 1] (using MATLAB notation- I couldn't figure out how to put in proper matrix notation).
Homework Equations
I find the eigenvectors as 4.2361 and -0.2361
For eigenvalue 4.2361: [3 2; 2 1] - [4.2361 0; 0 4.2361] = [-1.2361 2; 2 -3.2361]
-1.2361x1 + 2x2 = 0
x2 = 0.6180 x1
Therefore eigenvector: (1 0.6180) and normalizing it: (0.8506 0.5257)
For eigenvector -0.2361: Eigenvector: (1 -1.6180) and normalizing it: (0.5257 -0.8506)
Therefore my orthonormal basis of eigenvectors:
(0.8506 0.5257; 0.5257 -0.8506)
First Question:
Is what the question is asking - to get an orthonormal basis of eigenvectors. Is this what I am doing?
Second Question:
I think it is but when I compare my answer to MATLAB, for eigenvector 4.2361, MATLAB gives normalized eigenvectors (-0.8506 -0.5257).
I don't understand where the negative comes from.
Thanks
Asif