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WordNet-Online
Definitions from WordNet | ||||
Definitions from the WebHilbert SpaceA Hilbert space, named after the German mathematician David Hilbert, is a complete inner product space equipped with a specific mathematical structure. Senses and Usages:NounSense: A mathematical concept Usage: In mathematics, a Hilbert space is a complete inner product space that plays a crucial role in functional analysis, quantum mechanics, and harmonic analysis. Example Sentence: The concept of Hilbert space provides a framework to reason about infinite-dimensional vector spaces. NounSense: A concept in physics Usage: In physics, a Hilbert space is utilized to abstractly represent the state of a quantum mechanical system, where each vector in this space corresponds to a possible state of the system. Example Sentence: The wave function of a particle can be represented as a vector in a Hilbert space. Related Products: | ||||
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