Definition of Hilbert space in English: Hilbert space

noun Mathematics An infinite-dimensional analog of Euclidean space.

Example sentences

‘He took various ideas of Hilbert on integral equations and combined these into the concept of a Hilbert space around 1905.’ ‘His theorem, now called the Riesz - Fischer theorem, which he proved in 1907, is fundamental in the Fourier analysis of Hilbert space.’ ‘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.’ ‘In 1943 he proved the Gelfand Naimark theorem on self-adjoint algebras of operators in Hilbert space.’ ‘They showed that these rings could always be represented as a ring of linear operators on a Hilbert space.’ Origin Early 20th century: named after David Hilbert (1862–1943), German mathematician.

Pronunciation Hilbert space /ˈhilbərt ˌspās/