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- Singular_value abstract "In mathematics, in particular functional analysis, the singular values, or s-numbers of a compact operator T : X → Y acting between Hilbert spaces X and Y, are the square roots of the eigenvalues of the non-negative self-adjoint operator T*T : X → X (where T* denotes the adjoint of T).The singular values are non-negative real numbers, usually listed in decreasing order (s1(T), s2(T), …). If T is self-adjoint, then the largest singular value s1(T) is equal to the operator norm of T (see Courant minimax principle).In the case that T acts on euclidean space Rn, 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 (the figure provides an example in R2).In the case of a normal matrix A, the spectral theorem can be applied to obtain unitary diagonalization of A as per A = UΛU*. Therefore, and so the singular values are simply the absolute values of the eigenvalues.Most norms on Hilbert space operators studied are defined using s-numbers. For example, the Ky Fan-k-norm is the sum of first k singular values, the trace norm is the sum of all singular values, and the Schatten norm is the pth root of the sum of the pth powers of the singular values. Note that each norm is defined only on a special class of operators, hence s-numbers are useful in classifying different operators.In the finite-dimensional case, a matrix can always be decomposed in the form UDW, where U and W are unitary matrices and D is a diagonal matrix with the singular values lying on the diagonal. This is the singular value decomposition.".
- Singular_value thumbnail Singular_value_decomposition.gif?width=300.
- Singular_value wikiPageID "709116".
- Singular_value wikiPageRevisionID "597643572".
- Singular_value hasPhotoCollection Singular_value.
- Singular_value subject Category:Operator_theory.
- Singular_value subject Category:Singular_value_decomposition.
- Singular_value comment "In mathematics, in particular functional analysis, the singular values, or s-numbers of a compact operator T : X → Y acting between Hilbert spaces X and Y, are the square roots of the eigenvalues of the non-negative self-adjoint operator T*T : X → X (where T* denotes the adjoint of T).The singular values are non-negative real numbers, usually listed in decreasing order (s1(T), s2(T), …).".
- Singular_value label "Singular value".
- Singular_value label "Valore singolare".
- Singular_value label "قيمة فردية".
- Singular_value label "特異値".
- Singular_value sameAs Valore_singolare.
- Singular_value sameAs 特異値.
- Singular_value sameAs m.034ppp.
- Singular_value sameAs Q4166054.
- Singular_value sameAs Q4166054.
- Singular_value wasDerivedFrom Singular_value?oldid=597643572.
- Singular_value depiction Singular_value_decomposition.gif.
- Singular_value isPrimaryTopicOf Singular_value.
