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Hilbert Space

Named for mathematician David Hilbert, a Hilbert space is a generalization of Euclidian geometry useful for formalizing vectors and vector fields for the purpose of analysis. In quantum mechanics where observable quantities are modeled by linear equations and linear transformations, the use of Hilbert space geometry is truly fundamental.

Rather than the dot product representations of ordinary Euclidian space of limited dimensions, the fundamental objects in Hilbert space are abstractions of functional vectors in as many dimensions as apply. These can be multiplied by scalars and the product in Hilbert space will be a complete description, even in infinite dimensions. A large range of linear problems can be represented in specified Hilbert space and analyzed in simple geometric terms.

Web Resources On Hilbert Space

http://en.wikipedia.org/wiki/Hilbert_space
http://us.metamath.org/mpegif/mmhil.html

Book Resources On Hilbert Space

Principles of Linear Systems by Philip E. Sarachik
Geometric Algebra for Physicists by Chris Doran and Anthony Lasenby

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