Eigenvector Algor differences?

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In summary, the conversation discusses the differences in results obtained from different eigenvector algorithms, specifically between QL with implicit shifts from Numerical Recipes and Matlab's LAPACK routines. The question of whether Matlab's LAPACK uses a specific method and where to find the source code in c++ is also raised. The response clarifies that eigenvectors are not always unique and can vary depending on algorithm choices, giving an example of linearly independent eigenvectors with the same eigenvalue.
  • #1
disillusioned
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Hi,

Does different eigenvector algorithm give different result?
eg. using QL with implicit shifts frm (Numerical Recipes) vs Matlab's LAPACK routines?

or anyone knows what method Matlab's LAPACK uses & where i can find the source code in c++?

Are eigenvectors unique?

Thanks!
 
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  • #2
I don't know what algoritms you mean and I`m not that familiar with Matlab.

Anyway, different eigenvalues always correspond to linearly independent eigenvectors.
But it is possible to have two linearly independent eigenvectors corresponding to the same eigenvalue.

Hope that helps.
 
  • #3
disillusioned said:
Are eigenvectors unique?
No they're not. Depending on arbitrary choices made while using whatever algorithm you choose you can end up with a different set of eigenvectors than someone else doing the same problem. As a simple example, if [1,2,3] is your eigenvector and [2,4,6]=2[1,2,3] is your friend's, they're both right (assuming one of them is!).
 
  • #4
look, take the identity map. then anything is an eigenvector (except zero). so what do you mean by unique"
 

1. What is an eigenvector?

An eigenvector is a vector that does not change direction when a linear transformation is applied to it. In other words, it is a special vector that remains parallel to its original direction even after a transformation is applied.

2. What is an eigenvalue?

An eigenvalue is a scalar that represents how much an eigenvector is stretched or compressed by a linear transformation. It is often denoted by the Greek letter lambda (λ).

3. What is the significance of eigenvectors and eigenvalues?

Eigenvectors and eigenvalues are used to understand the behavior of linear transformations, such as rotations and scaling. They also have important applications in fields such as engineering, physics, and computer science.

4. What is the difference between eigenvectors and eigenvector algorithms?

An eigenvector is a vector, while an eigenvector algorithm is a method used to find eigenvectors and eigenvalues. Eigenvector algorithms, such as the power method and the QR algorithm, use mathematical techniques to iteratively compute eigenvalues and eigenvectors.

5. How are eigenvector algorithms used in data analysis?

Eigenvector algorithms are commonly used in data analysis to reduce the dimensionality of a dataset and identify the most important patterns and relationships. They can also be used in machine learning algorithms, such as principal component analysis, to extract features and reduce noise in data.

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