MATLAB: Eig versus svd functions

eig

Hi,

I would like to ask what is the difference between the function eig and svd and what is the difference between the right eigenvectors and the right singular eigenvectors of these functions?

Thank you

Best Answer

SVD is a decomposition for arbitrary-size matrices, while EIG applies only to square matrices. They are very much related:

The right singular vectors of A are the eigenvectors of A'*A, and the left singular vectors of A are the eigenvectors of A*A'.

Similarly the singular values of A are the square root of the eigenvalues of A*A' (or A'*A, the eigenvalues of those are just the same)

Related Solutions

MATLAB: How to find all the eigenvectors of a very large, sparse, symmetric, positive-definite matrix in MATLAB 7.8 (R2009a)

You are receiving the out of memory error because EIGS tries to return all of the eigenvectors at once and it is not possible to store all the 22500 eigenvectors on a 32-bit machine.

As a workaround, knowledge of the eigenvalues can be used to access the eigenvectors in chunks using the function EIGS as follows:

[V D] = eigs(A,100,0);

The above code will give 100 eigenvectors corresponding to eigenvalues closest to 0. For better results, never use an eigenvalue as the shift (third argument in EIGS).

When retreiving the eirgenvectors, note that although the matrix is sparse the eigenvectors are most likely dense.

MATLAB: Eigenvalues and orthonormal eigenvectors

Yes there is. Look at the eig function.

Best Answer

Related Solutions

MATLAB: How to find all the eigenvectors of a very large, sparse, symmetric, positive-definite matrix in MATLAB 7.8 (R2009a)

MATLAB: Eigenvalues and orthonormal eigenvectors

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