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  "body": "\n## Summary\n\nThe point spectrum of an operator is its set of eigenvalues.\nIt is the part of the [[spectrum|BMKATJ802A]] where $T - \\lambda I$ fails to be injective.\nFor matrices the point spectrum is the whole spectrum, but in infinite dimensions it can be a small part of it, or empty.\n\n## Explanations\n\n### L1 human\n\nAn eigenvalue $\\lambda$ is a number for which some nonzero vector is just multiplied by $\\lambda$.\nThe point spectrum collects these numbers.\nFor the left shift $(x_1, x_2, \\ldots) \\mapsto (x_2, x_3, \\ldots)$ on square-summable sequences, the sequence $(1, \\lambda, \\lambda^2, \\ldots)$ is an eigenvector for every $\\abs{\\lambda} \u003c 1$.\nFor the right shift, which only moves entries further out, there are no eigenvalues at all.\n",
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