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  "body": "\n## Summary\n\nFor $1 \\le p \u003c \\infty$, the Schatten $p$-class consists of the compact operators on a Hilbert space whose sequence of singular values is $p$-summable.\nThese classes are the operator analogues of the sequence spaces $\\ell^p$.\nThe case $p = 1$ is the trace class and the case $p = 2$ is the Hilbert–Schmidt class, the two most used ideals of operators.\n\n## Explanations\n\n### L1 human\n\nA compact operator has a sequence of singular values that tends to zero, like the stretch factors of a matrix.\nThe Schatten classes sort compact operators by how fast these numbers decrease.\nAn operator lies in the $p$-class when the sum of the $p$-th powers of its singular values is finite.\nFor example, the diagonal operator with entries $1/n$ lies in the $p$-class exactly when $p \u003e 1$, because $\\sum 1/n^p$ converges exactly then.\n",
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