Hilbert space - Wikipedia
In mathematics, Hilbert spaces (named after David Hilbert) allow the methods of linear algebra and calculus to be generalized from (finite-dimensional) Euclidean vector spaces to spaces …
希尔伯特空间 - 维基百科，自由的百科全书
在 数学 裡， 希尔伯特空间 （英語： Hilbert space）即 完备的内积空间，也就是一個帶有 內積 的 完備 向量空間。 內積的構造推廣了 欧几里得空间 的 距离 和 角 的概念；完備則確保了其上 …
Hilbert Space -- from Wolfram MathWorld
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. If the metric defined by the norm is not …
convenience in in nite dimensional vectors’ analysis, Hilbert space has been widely used in other elds, for example physicians applied this concept in quantum mechanics, economists even …
Definition 1.1. A Hilbert space is a vector space V with an inner product satisfying (1.1) - (1.4) which is complete as a normed space (i.e., is a Banach space). Thus we have already shown …
There are really three `types' of Hilbert spaces (over C): The nite dimensional ones, essentially just Cn; with which you are pretty familiar and two in nite dimen-sional cases corresponding to …
Definition 12.7. A Hilbert space is an inner product space (H,h·,·i) such that the induced Hilbertian norm is complete. Example 12.8. Let (X,M,µ) be a measure space then H:= …
There are really three `types' of Hilbert spaces (over C): The nite dimen-sional ones, essentially just Cn; for di erent integer values of n; with which you are pretty familiar, and two in nite …
Hilbert Space | Brilliant Math & Science Wiki
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 …
Last time, we introduced the concept of a pre-Hilbert space (a vector space that comes equipped with a Hermitian inner product). This inner product is positive definite, linear in the first …