Hilbert space
[/ˈhɪlbərt speɪs/]
nounpl: Hilbert spaces
espaço de Hilbert
1. A complete infinite-dimensional vector space equipped with an inner product, forming the mathematical foundation for quantum mechanics and functional analysis
The wave functions in quantum mechanics are represented as vectors in a Hilbert space.
As funções de onda na mecânica quântica são representadas como vetores em um espaço de Hilbert.
2. A mathematical structure that generalizes Euclidean space to infinite dimensions while preserving geometric and algebraic properties
Hilbert spaces allow mathematicians to study infinite-dimensional linear algebra rigorously.
Os espaços de Hilbert permitem que matemáticos estudem álgebra linear infinito-dimensional de forma rigorosa.
The term 'espaço de Hilbert' is a technical term used primarily in academic and research contexts across Portuguese-speaking countries. It is named after German mathematician David Hilbert and is fundamental to both Brazilian and Portuguese mathematical education, particularly in advanced courses in functional analysis, quantum mechanics, and mathematical physics.
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