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I have been wanting to calculate eigenvalues and eigenvectors for a non-square matrix and I know that svd method is used.
But, given my poor background, I don't understand how to figure out eigenvalues and eigenvectors from the u, d and v matrices.
According to the man page, svd returns a list with the following elements:
- d: a vector containing the singular values of x, of length min(n, p).
- u: a matrix whose columns contain the left singular vectors of x, present if nu 0. Dimension c(n, nu).
- v: a matrix whose columns contain the right singular vectors of x, present if nv 0. Dimension c(p, nv).
Wikipedia describes the relation between Eigendecomposition and SVD as follows: Given the SVD of $M$
$$M = U \; \Sigma \; V^*,$$
then
- The left singular vectors of $M$ are eigenvectors of $MM^*$.
- The right singular vectors of $M$ are eigenvectors of $M^*M$.
- The non-zero singular values of $\Sigma$ are the square roots of the non-zero eigenvalues of $M^*M$ or $MM^*$.
Does that help answer your question on how to identify the results returned by svd?
