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Definition of Hilbert space
1. Noun. A metric space that is linear and complete and (usually) infinite-dimensional.
Definition of Hilbert space
1. Noun. (functional analysis) A generalized Euclidean space in which mathematical functions take the place of points; crucial to the understanding of quantum mechanics and other applications. ¹
¹ Source: wiktionary.com
Lexicographical Neighbors of Hilbert Space
Literary usage of Hilbert space
Below you will find example usage of this term as found in modern and/or classical literature:
1. Quantum Statistical Mechanics and Lie Group Harmonic Analysis by Norman Hurt, Robert Hermann (1980)
"A Hilbert space SETTING FOR DISCRETE SPECTRA STATISTICAL MECHANICS PROBLEMS Let
Jr be a complex Hilbert space, in the usual functional analysis setting. ..."
2. Proceedings of the Berkeley-Ames Conference on Nonlinear Problems in Control by L. R. Hunt, Clyde Martin (1984)
"Here we pose the same problem In a separable Hilbert space. From the autonomous
case we know that in general it Is not possible to transfer stabilizability ..."
3. Cartanian Geometry, Nonlinear Waves, and Control Theory. by Robert Hermann (1980)
"From the Hilbert space point of view, it is natural to interpret (3.4) from the
following point of view: Set <x1,x2> = x1 x2 (3.5) 3 for x1,x2 € R This ..."
4. Real Analysis by Andrew M. Bruckner, Judith B. Bruckner, Brian S. Thomson (1997)
"15.11 Fourier Series in Hilbert space We have come far enough in our study of
Fourier ... In the Hilbert space L^T), all these things are true and more. ..."
5. Topics in Physical Geometry by Robert Hermann (1988)
"A BASIC QUANTUM MECHANICAL/ALGEBRAIC FRAMEWORK I will take the physicist attitude
toward the fundamentals of the Hilbert space approach to quantum ..."
6. Differential Geometry in Statistical Inference by Shunʼichi Amari (1987)
"Thus, HU is a Hilbert space. Since the tangent vectors M(x,u), which span T,,(M),
satisfy E[3 i] = 0, E[(3 i)2] = g,,(u)<», ..."
7. Topics in the Mathematics of Quantum Mechanics by Robert Hermann (1973)
"QUANTUM OBSERVABLES AS FUNCTIONS ON COMPLEX PROJECTIVE SPACE The complex protective
space associated with a Hilbert space is important for quantum mechanics ..."
8. Useful Knowledge: The American Philosophical Society Millennium Program by Alexander G. Bearn, American Philosophical Society (1999)
"So, for example, if the experiment is just to flip a coin and the only possible
results are heads or tails, then Hilbert space will be a two-dimensional ..."
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