Singular Values (s-numbers)
- 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 (necessarily non-negative) eigenvalues of the self-adjoint operator (𝑇†𝑇) (where 𝑇† denotes the hermitian adjoint of 𝑇)
- the singular values of 𝑇 are non-negative real numbers, usually listed in decreasing order (𝜎1(𝑇), 𝜎2(𝑇), …)
- the largest singular value of 𝑇 is equal to the operator norm of 𝑇