Hi, How to obtain eigenvalue of a matrix using fft function and eigenvector using DFT function?

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.

Thank you.

Answer 1

[pbag47]

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If A is not a circulant matrix, then this process is no longer valid I guess.