Hilbert space


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

Recent Examples on the Web Because quantum matter lives in this exponentially large Hilbert space. Steven Strogatz, Quanta Magazine, 3 May 2023 Its Hilbert space consists of all possible combinations of amplitudes in the two locations. Charlie Wood, Quanta Magazine, 26 Sep. 2022 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

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'Hilbert space.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

Word History


David Hilbert

First Known Use

1911, in the meaning defined above

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

Dictionary Entries Near Hilbert space

Cite this Entry

“Hilbert space.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/Hilbert%20space. Accessed 19 May. 2024.

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