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  "body": "\n## Summary\n\nThe spectrum of a bounded operator $T$ on a complex Banach space is the set of complex numbers $\\lambda$ for which $T - \\lambda I$ is not invertible.\nIt generalises the set of eigenvalues of a square matrix, the [[spectrum of a matrix|0XPX5NC67E]].\nIn infinite dimensions it can contain numbers that are not eigenvalues.\nIt is always a nonempty compact subset of the plane when the space is not zero.\n\n## Explanations\n\n### L1 human\n\nFor a matrix, $\\lambda$ is an eigenvalue exactly when $A - \\lambda I$ cannot be inverted.\nThe spectrum keeps this second description and uses it for operators in infinite dimensions.\nThere, $T - \\lambda I$ can fail to be invertible even when it is injective, because it may miss some vectors.\nFor the right shift on square-summable sequences, there are no eigenvalues, yet the spectrum is the whole closed unit disc.\n",
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