Hilbert space
Vector algebra and calculus are methods normally used in the two-dimensional Euclidean plane and three-dimensional space. In Hilbert spaces, these methods can be used with any finite or infinite number of dimensions. A Hilbert space is a vector space that has the structure of an inner product that allows length and angle to be measured. Hilbert spaces also have to be complete, which means that enough limits have to exist for calculus to work.