What is the difference between “singular value” and “eigenvalue”?

I am trying to prove some statements about singular value decomposition, but I am not sure what the difference between singular value and eigenvalue is.

Is “singular value” just another name for eigenvalue?

Answer

The singular values of a M×N matrix X are the square roots of the eigenvalues of the N×N matrix XX (where stands for the transpose-conjugate matrix if it has complex coefficients, or the transpose if it has real coefficients).

Thus, if X is N×N real symmetric matrix with non-negative eigenvalues, then eigenvalues and singular values coincide, but it is not generally the case!

Attribution
Source : Link , Question Author : Ramon , Answer Author : The Phenotype

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