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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?

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    They agree in finite dimensions, but not necessarily for infinite-dimensional operators. I've heard the term "singular value" applied to any value for which $(A-\lambda I)^{-1}$ either does not exist or is not continuous, while eigenvalues refer only to those values for which $(A-\lambda I)^{-1}$ does not exist.2012-04-03
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    The singular value is a nonnegative scalar of a square or rectangular matrix while an eigenvalue is a scalar (any scalar) of a square matrix.2012-04-03
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    ^Note that I was addressing square matrices specifically, or in the infinite-dimensional case, endomorphisms.2012-04-03
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    My guess is that the question is about the singular value decomposition for matrices of finite-dimensional operators.2012-04-03
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    They are not the same thing at all, and has nothing to do with dimension. They only agree in the special case where the matrix is symmetric. This agreement also extends (in a sense) for infinite dimensional compact operators.2012-09-30
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    @AlexBecker Perhaps you are thinking of the singular spectrum of an infinite dimensional operator instead? (an unrelated topic)2012-09-30
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    @AlexBecker : The DO NOT agree in finite dimensions! Clearly you're not familiar with the singular value decomposition. All real matrices have singular values, but non-square matrices don't have eigenvalues.2013-01-23

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