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An infinite-dimensional Hilbert space is a mathematical concept that has properties such as being complete, having an inner product, and being separable. It is commonly used in quantum mechanics and functional analysis to study functions and vectors in an infinite-dimensional space. Applications include quantum mechanics, signal processing, and machine learning.

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What is the significance of Hilbert space in the context of quantum mechanics?

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Related Questions

Let H be a separable Hilbert space?

Yes, you could let H be a separable Hilbert space. Then what?


What has the author Lokenath Debnath written?

Lokenath Debnath has written: 'Nonlinear Partial Differential Equations for Scientists and Engineers' 'Wavelet Transforms and Their Applications' 'Introduction to Hilbert spaces with applications' -- subject(s): Hilbert space 'Nonlinear water waves' -- subject(s): Water waves, Nonlinear waves 'Wavelet Transforms & Time-Frequency Signal Analysis'


Prove that Hilbert Space is a Metric Space?

The question doesn't make sense, or alternatively it is true by definition. A Hilbert Space is a complete inner product space - complete in the metric induced by the norm defined by the inner product over the space. In other words an inner product space is a vector space with an inner product defined on it. An inner product then defines a norm on the space, and every norm on a space induces a metric. A Hilbert Space is thus also a complete metric space, simply where the metric is induced by the inner product.


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What is the significance of Hilbert space in the context of quantum mechanics?

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What has the author N I Akhiezer written?

N. I. Akhiezer has written: 'Theorie der linearen Opteratoren im Hilbert-Raum' -- subject(s): Hilbert space 'Theorie der linearen Operatoren im Hilbert-Raum' -- subject(s): Hilbert space, Linear operators, Functional analysis 'Lectures on integral transforms' -- subject(s): Integral transforms 'Elements of the theory of elliptic functions' -- subject(s): Elliptic functions


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When was Space Applications Centre created?

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What is the significance of the Hilbert-Schmidt inner product in the context of functional analysis?

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