Hilbert space
- Category
- STANDARD MATHEMATICS
- Definition
- A complete inner-product space providing a geometric framework for functions, vectors and operators.
- Math Level
- SPECIALIST
A Hilbert space is a complete vector space equipped with an inner product.
It generalises ordinary Euclidean geometry to settings that may have infinitely many dimensions. Positive-definite kernels and several RH-equivalent positivity frameworks can naturally be expressed using Hilbert-space geometry.
See also: vector, inner product, positive definiteness, kernel..