I often encounter the unfamiliar and familiar term Hilbert Space and decide to solve this term.
1 Shorthand
Hilbert space is the linear space based on the added three conditions, i.e. completeness , infinite-dimensional and product operation to meet the formation of new space.
2 understand
Hilbert Space: It is complete , may be of infinite dimensions , and is given a linear space for inner product operations .
Linear space: the vector space on linear algebra, that is, it satisfies the closed points and multiplication. The detailed nature is as follows:
Complete: The limit operation is closed, that is, the limit value when n approaches to infinity, also in Hilbert space
Unlimited dimensions: Dimensions without limit , we often use the Euclidean space, two-dimensional.
Inner product: high school concept, two vectors are correspondingly multiplied and added. The inner product operation needs to be symmetric, semi-definite and linear.
(Source: Whiteboard Book)