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  "body": "\n## Summary\n\nA degenerate kernel is a [[kernel|GSMBXT7FPK]] that is a finite sum of products $a_i(x) b_i(s)$ of functions of one variable.\nIt is also called a separable kernel or a kernel of finite rank, since its integral operator is a [[finite-rank operator|Z8FABSYQTS]].\nAn integral equation of the second kind with a degenerate kernel reduces to a finite [[system of linear equations|0GT4WWGWH2]].\nApproximating a general kernel by degenerate ones is a main route to Fredholm theory and to numerical methods.\n\n## Explanations\n\n### L1 human\n\nA degenerate kernel splits into finitely many pieces, each a function of $x$ times a function of $s$.\nThen the integral in the equation only produces finitely many unknown numbers, the integrals $\\int b_i \\varphi$.\nSolving for these numbers is plain linear algebra.\nFor example, $K(x, s) = 1 + x s$ is degenerate with two terms, while $e^{x s}$ is not degenerate.\n",
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