Definition: Hilbert Space

A Banach space \((V,||~||)\), in which the norm \([||~||"\) is given by the square root \[||~||:=\sqrt{\langle\cdot,\cdot\rangle},\] where \(\langle\cdot,\cdot\rangle\) is a positive definite dot product is called a Hilbert space, named after the German mathematician David Hilbert (1862 - 1943).

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  1. Wille, D; Holz, M: "Repetitorium der Linearen Algebra", Binomi Verlag, 1994