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Linear map (linear operator)

| 🗖 nosplit | ↑ parent "Matrix multiplication" | words: 191 | descendant words: 205 | descendants: 2
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A linear function from where and are vector spaces.
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Basically a generalization of both:
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The key advantage over those concepts however is that it makes more sense in infinite dimensional spaces like Hilbert spaces.
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Calling such functions "matrices" in infinite dimensions is stretching it a bit, since we would need to specify infinitely many rows and columns.
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The key building block of infinite dimensional linear map is the derivative. In that case, the vectors being operated upon are functions, which cannot therefore be specified by a finite number of parameters.
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For example, the left side of the time-independent Schrodinger equation is a linear map. And the time-independent Schrodinger equation can be seen as a eigenvalue problem.
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Ancestors

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