Hilbert space is a fundamental concept in functional analysis, which is a branch of mathematics that studies functions and their properties. It is named after the German mathematician David Hilbert, who first introduced the concept in the early 20th century.
A Hilbert space is a complete inner product space, which means that it is a vector space equipped with an inner product that is also a complete metric space. This inner product satisfies certain properties, including symmetry, linearity in the first argument, and positive definiteness. The completeness of the space means that any Cauchy sequence of vectors in the space has a limit that is also in the space.
Hilbert Space Notes. The study of functions and the qualities they possess falls within the purview of the mathematical discipline known as functional analysis. Hilbert space is an essential notion in this domain. David Hilbert, a German mathematician, is credited with being the one who initially presented the idea in the early 20th century. As … Read more
