Singular Value
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High Quality Content by WIKIPEDIA articles! In mathematics, in particular functional analysis, the singular values, or s-numbers of a compact operator T acting on a Hilbert space are defined as the eigenvalues of the operator sqrt{T^ T} (where T denotes the adjoint of T and the square root is taken in the operator sense). The singular values are nonnegative real numbers, usually listed in decreasing order s1(T), s2(T), ... . The largest singular value s1(T) is equal to the operator norm of T. In the case that T acts on euclidian space mathbb{R}^n, there is a simple geometric interpretation for…mehr

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High Quality Content by WIKIPEDIA articles! In mathematics, in particular functional analysis, the singular values, or s-numbers of a compact operator T acting on a Hilbert space are defined as the eigenvalues of the operator sqrt{T^ T} (where T denotes the adjoint of T and the square root is taken in the operator sense). The singular values are nonnegative real numbers, usually listed in decreasing order s1(T), s2(T), ... . The largest singular value s1(T) is equal to the operator norm of T. In the case that T acts on euclidian space mathbb{R}^n, there is a simple geometric interpretation for the singular values: Consider the image by T of the unit sphere; this is an ellipsoid, and its semi-axes are the singular values of T.