Numerical Recipes In C Eigenvectors Calculation (from Numerical Recipes In C Book)?
Eigenvectors calculation (from Numerical Recipes in C book)? - numerical recipes in c
Hello,
I have implemented the algorithms tred2 () (page 474) and tqli () (page 480) to compute the eigenvalues and eigenvectors of real matrices and compare the results with those obtained with Matlab, some of the eigenvectors of opposite sign. Each value is good, but it seems that the vector is multiplied by -1.
Who knows what it is and whether it really a mistake?
Thank you in advance.
PS: The book is available online at
http://www.nr.com/nronline_switcher.php
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1 comments:
Eigenvectors are not unique. If the matrix is an eigenvector of
[1, -2]
For example, if each multiple of this eigenvector is an eigenvector is the hypothetical matrix, and
[2 -4]
[50, -100]
[-1, 2]
[-1000, 2000] "
Eigenvectors of this hypothetical matrix. The reason is a square matrix eigenvector x corresponding eigenvalue λ for some constant c
A (c * x) = C * A *
C * = λx
Λ = (c * x)
This means that c * x is an eigenvector of A.
Therefore, no error. Some are simply multiplied by -1. You're good.
Edit: No, stay, the eigenvalues unchanged. Note: cyx was used in the proof of my "on the same eigenvalue λ * vector x. As I said earlier, eigenvectors are not unique, even for a certain intrinsic value.
Here is an example.
A =
[4 -2]
[1 1]
x =
[2]
[1]
Ax =
[6]
[3]
= 3x
So x is a is own finalector of A with a value of 3 Let now y =- x = [-2 -1].
Ay =
[-6]
[-3]
= 3y
So y =- x is an eigenvector of A with an eigenvalue of 3
I can not message you, send me a message if you have any questions.
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