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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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