Hilbert space
1
9.9
- noun
- /ˈhɪl.bɜrt speɪs/
- Specialized
:
espacio de Hilbert
- The mathematical framework of quantum physics is built upon the properties of Hilbert space.
It's a Hilbert space that is composed of two elements.
- It's a Hilbert space that is composed of two elements.
- Not you know, the most important thing of a Hilbert space is this norm, this inner product.
- But V converges requires that it converge for any function of Hilbert space.
Examples
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But when asked to describe this material world, you are probably going to say, very rightly, that it is all just quantum fields and state vectors evolving in a Hilbert space.
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In quantum mechanics, the state of a particle is represented as a vector in a Hilbert space.
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It's a Hilbert space that is composed of two elements.
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Most I think all of the Hilbert spaces you've come into contact with are separable.
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First, the phase space where the Earth system moves on a dynamical orbit is an infinite-dimensional Hilbert space.
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When studying functional analysis, one often encounters various types of Hilbert spaces.
Surface Forms
Morphology
Hilbert + space
This is an eponymous technical term: 'Hilbert' is a proper name (a mathematician) and 'space' in everyday English means an area, so knowing the constituents does not allow a B1 learner to infer the specialized mathematical meaning (complete linear metric space with inner-product structure). Cross-linguistically such named technical constructs require subject-matter knowledge rather than compositional inference, so the expression is not transparently derivable from its parts.
Etymology
Hilbert space is named after the mathematician David Hilbert, and space here is a way to say a 'room' for mathematical objects. Imagine a room where arrows can still have 'distance' and 'right angles' even if the room is very large, and that's why scientists use Hilbert space to make the ideas of ordinary geometry work for things like quantum physics.