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  "body": "\n## Summary\n\nThe spectrum of an element $a$ of a unital algebra is the set of scalars $\\lambda$ for which $a - \\lambda 1$ has no inverse.\nFor square matrices it is the set of eigenvalues, and for bounded operators it can be larger than the set of eigenvalues.\nIn a complex Banach algebra the spectrum is a nonempty compact set.\nIt is the starting point of spectral theory and of the functional calculus.\n\n## Explanations\n\n### L1 human\n\nFor a matrix $a$, the number $\\lambda$ is an eigenvalue exactly when $a - \\lambda$ cannot be inverted.\nThe spectrum keeps this second description and uses it in any algebra where one can multiply and invert.\nFor a continuous function $f$ on $[0,1]$, the function $f - \\lambda$ has an inverse exactly when it never vanishes.\nSo the spectrum of $f$ is the set of values of $f$.\n",
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