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What's A Hilbert Space


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What's A Hilbert Space. So in inner product space, we also. It is an extension of euclidean space for infinite dimensions.

What's a Hilbert space? A visual introduction YouTube
What's a Hilbert space? A visual introduction YouTube from www.youtube.com

David hilbert and john von neumann both played played key roles in the development of hilbert. So in inner product space, we also. A hilbert space is a vector space h with an inner product <f,g> such that the norm defined by |f|=sqrt (<f,f>) turns h into a complete metric space.

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What's a Hilbert space? A visual introduction YouTube

A hilbert space is a vector space \ (v\) equipped with an inner product, which can be thought of as a generalization of the dot product in euclidean space, with the additional property that the metric coming from the inner product makes \ ( v\) into a complete metric space. As we noted before, inner product space or hilbert space can be viewed as a generalization of linear vector space. Hilbert space is a mathematical space proposed by david hilbert, german mathematician. If the metric defined by the norm is not complete, then h is instead known as an inner product space.

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