Hi, How to obtain eigenvalue of a matrix using fft function and eigenvector using DFT function?
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Hi,
I would like to solve a very large size of matrix using eigenvalue decomposition method where
A=F*lamda*F^H.
F denotes as eigenvector while lamda is the eigenvalues of the matrix. I tried to solve F using DFT,
. The eigenvalues, lamda is obtained based on the fft of the first column of matrix A. However, when I substitute these values in equation A, it did not work. It gives totally different answer as compared with the function of eig in matlab.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/208836/image.png)
Thank you.
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Answers (1)
pbag47
on 15 Jan 2024
Hello,
To my knowledge and understanding, this technique only works if A is a circulant matrix. In this case, the DFT of each column gives the same output which leads to the eigenvalues of A (up to a multiplying constant that depends on the scaling factor chosen with the fft function).
If A is not a circulant matrix, then this process is no longer valid I guess.
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