Hilbert space

noun

Hil·​bert space ˈhil-bərt- How to pronounce Hilbert space (audio)
: a vector space for which a scalar product is defined and in which every Cauchy sequence composed of elements in the space converges to a limit in the space

Examples of Hilbert space in a Sentence

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That’s all well and good, but our Universe isn’t well-described as a physical Hilbert space, so that isn’t a compelling argument. Ethan Siegel, Big Think, 8 Aug. 2025 Because quantum matter lives in this exponentially large Hilbert space. Steven Strogatz, Quanta Magazine, 3 May 2023 Instead it is found in a 4-D mathematical entity called a Hilbert space. Davide Castelvecchi, Scientific American, 8 Feb. 2022 This is most clear with the many-worlds interpretation of quantum mechanics, which says that the world is described by a state in a Hilbert space evolving according to the Schrodinger equation and that's it. Sean Carroll, Discover Magazine, 4 June 2012

Word History

Etymology

David Hilbert

First Known Use

1911, in the meaning defined above

Time Traveler
The first known use of Hilbert space was in 1911

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Cite this Entry

“Hilbert space.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/Hilbert%20space. Accessed 8 Sep. 2025.

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