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  "body": "\n## Summary\n\nThe singular values of a compact operator $T$ between Hilbert spaces are the eigenvalues of the positive operator $\\abs{T} = (T^* T)^{1/2}$, listed in decreasing order.\nThey extend the singular values of matrices to infinite dimensions and form a sequence that tends to $0$.\nThey measure how well $T$ can be approximated by finite-rank operators.\nTheir rate of decay defines the Schatten classes, among them the trace class and the Hilbert–Schmidt operators.\n\n## Explanations\n\n### L1 human\n\nA compact operator stretches the unit ball into an infinite-dimensional ellipsoid whose axes shrink to zero.\nThe singular values are the lengths of these semi-axes, from the longest to the shortest.\nFor example, the operator on square-summable sequences that multiplies the $n$-th coordinate by $(-1)^n / n$ has singular values $1, 1/2, 1/3, \\ldots$.\nThe faster the singular values decrease, the closer the operator is to a matrix of small size.\n",
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