Hilbert space, a generalization of the concept of Euclidean vector space, i.e., of a finite-dimensional real vector space equipped with a scalar product. A Hilbert space H [7–12] is a vector space over the real or complex numbers (sometimes over the quaternions) in which a scalar product is defined and which is complete w.r.t. the norm induced by the scalar product.
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Scholz, E., Stulpe, W. (2009). Hilbert Space. In: Greenberger, D., Hentschel, K., Weinert, F. (eds) Compendium of Quantum Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70626-7_90
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