Definition of Hilbert space in English:

Hilbert space

nounˈhɪlbət speɪsˈhilbərt ˌspās

Mathematics

An infinite-dimensional analogue of Euclidean space.
〔数〕希尔伯特空间
Example sentencesExamples
- 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 1943 he proved the Gelfand Naimark theorem on self-adjoint algebras of operators in 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.
- 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.

Definition of Hilbert space in US English:

Hilbert space

nounˈhilbərt ˌspās

Mathematics

An infinite-dimensional analog of Euclidean space.
〔数〕希尔伯特空间
Example sentencesExamples
- 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.
- His theorem, now called the Riesz - Fischer theorem, which he proved in 1907, is fundamental in the Fourier analysis of Hilbert space.
- 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.
- He took various ideas of Hilbert on integral equations and combined these into the concept of a Hilbert space around 1905.

Origin

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

词汇	Hilbert space
释义	Definition of Hilbert space in English: Hilbert space nounˈhɪlbət speɪsˈhilbərt ˌspās Mathematics An infinite-dimensional analogue of Euclidean space. 〔数〕希尔伯特空间 Example sentencesExamples 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 1943 he proved the Gelfand Naimark theorem on self-adjoint algebras of operators in 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. 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. Definition of Hilbert space in US English: Hilbert space nounˈhilbərt ˌspās Mathematics An infinite-dimensional analog of Euclidean space. 〔数〕希尔伯特空间 Example sentencesExamples 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. His theorem, now called the Riesz - Fischer theorem, which he proved in 1907, is fundamental in the Fourier analysis of Hilbert space. 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. He took various ideas of Hilbert on integral equations and combined these into the concept of a Hilbert space around 1905. Origin Early 20th century: named after David Hilbert (1862–1943), German mathematician.
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