Singular value
In mathematics, in particular in functional analysis, the singular values of a compact operator T : X → Y {\displaystyle \,T\! :X\rightarrow Y} acting between Hilbert spaces X {\displaystyle X} and Y {\displaystyle Y} , are the square roots of the (necessarily non-negative) eigenvalues of the self-adjoint operator T ∗ T {\displaystyle T^{*}T} (where T ∗ {\displaystyle T^{*}} denotes the adjoint of T {\displaystyle T} ). The singular values are non-negative real numbers, usually listed in decreasing order ( σ 1 ( T ) ≥ σ 2 ( T ) ≥ … ) {\displaystyle {\big (}\sigma _{1}(T)\geq \sigma _{2}(T)\geq \dots {\big )}} .