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  "body": "\n## Summary\n\nOperator theory is the part of functional analysis that studies linear operators between normed spaces, above all bounded operators on Banach and Hilbert spaces.\nIt asks how far the theory of matrices, with eigenvalues, adjoints and diagonalisation, extends to infinite dimensions.\nIts tools are used for differential and integral equations, quantum mechanics and signal processing.\n\n## Explanations\n\n### L1 human\n\nA matrix turns a vector of numbers into another vector of numbers.\nAn operator does the same thing for objects with infinitely many coordinates, such as sequences or functions.\nA good picture is the derivative, which turns a function into another function and respects sums and scalar multiples.\nA simple example is the right shift on sequences, $(x_1, x_2, \\ldots) \\mapsto (0, x_1, x_2, \\ldots)$.\nIt never loses information, yet it is not onto, something no square matrix can do.\nOperator theory explains such new effects of infinite dimension.\n",
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