Computing eigenvectors (from the book Numerical Recipes in C)?
Hi, I have implemented the algorithms tred2 () (page 474) and tqli () (page 480) for calculating eigenvectors and eigenvalues of real matrices, and comparing the results with those obtained with MatLab, some of the vectors themselves have the opposite sign. Each unique value is fine, but the vector appears to be multiplied by -1 .. Does anyone know what this is, and if this is really a failure PS? Thanks, in advance the book can be found online at http://www.nr.com/nronline_switcher. php Well, shoulnd't the values change accordingly? The eigenvalues are the same as Matlab, but some of the eigenvectors are (-1 thing)
Eigenvectors are not unique. If the matrix has an eigenvector [1, -2] 'for example, then any multiple of that eigenvector is also an eigenvector for this hypothetical array, so that [2, -4] "[50, -100] [-1, 2] '[-1000, 2000] are all eigenvectors of this hypothetical array. This is because for any square matrix A with corresponding eigenvector x to eigenvalues λ and for any constant C (c * x) = c * c = Ax-* lambda.x = λ (c * x) This means that c * x is an eigenvector of A. Therefore, no no error. Some are just multiplied by -1. You're good. Issue n, the values do not change. Note in my "proof" above is used the same value λ own vectors for X and C * x. As I said, are the only eigenvectors, even for an individual. Eigenvalue is not an example x. A = [4 -2] [1 1] = [2] [1] Ax = [6] [3] = 3x then x is an eigenvector of A with an eigenvalue of 3. Now let's look at y =- x = [-2 -1] '. Y = [-6] [-3] = 3 and therefore =- X is also an eigenvector of A with an eigenvalue of 3. I can not message you, so send me a message if you have any questions.
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