Definition of Hilbert space in English:

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Hilbert space

Pronunciation: /ˈhilbərt ˌspās/


An infinite-dimensional analog of Euclidean space.
Example sentences
  • His theorem, now called the Riesz - Fischer theorem, which he proved in 1907, is fundamental in the Fourier analysis of Hilbert space.
  • He took various ideas of Hilbert on integral equations and combined these into the concept of a Hilbert space around 1905.
  • In short, to have any hope of understanding what a Hilbert space is, you must learn and digest a whole hierarchy of lower-level concepts first.


Early 20th century: named after David Hilbert (1862–1943), German mathematician.

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