Hilbert Space. In this video, I introduce the Hilbert Space and describe its properties. The German mathematician David Hilbert first described this space in his.

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Hilbert spaces are the "most uniformly convex" and "most uniformly smooth" spaces in the sense that if X is any space whose dimension is at least two, then δH(∈)≥δX(∈) and ρH(τ)≤ρX(τ). A Hilbert space is a linear vector space about which you learn about in linear algebra. When using Hilbert spaces, we are particularly interested in orthogonal sub-spaces.

Space in maths, signifies a collection of vectors, which interact in a certain manner.

A Hilbert space is a (possibly) infinite-dimensional generalisation of the traditional spaces of Euclidean geometry in which the notions of distance and angle still make good sense.

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What is a Hilbert space? - Mathematics Stack Exchange

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Hilbert space - Encyclopedia of Mathematics

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REFLEXIVITY OF HILBERT SPACES (THEOREM: EVERY HILBERT SPACE IS REFLEXIVE) - YouTube

Hilbert space - Wikipedia

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Hilbert spaces are the natural abstract framework in which to study two important (and closely related) concepts: orthogonality and unitarity, allowing us to generalise familiar concepts and facts from. In mathematics, a Hilbert space is an inner product space that is complete with respect to the norm Hilbert spaces serve to clarify and generalize the concept of Fourier expansion and certain linear. A vector space defined over a field is equipped with two operations : a vector addition and a scalar multiplication.

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