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 ...Täielik kirjeldus
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.