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Hilbert Space

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A Hilbert space is a vector space that has a complete inner product. Hilbert spaces are important in the study of infinite-dimensional vector spaces.

Hilbert space is a college-level concept that would be first encountered in an analysis course covering functional analysis.

Prerequisites

Inner Product: (1) In a vector space, an inner product is a way to multiply vectors together, with the result being a scalar. (2) In vector algebra, the term inner product is used as a synonym for dot product.
Vector Space: A vector space is a set that is closed under finite vector addition and scalar multiplication. The basic example is n-dimensional Euclidean space.

Classroom Articles on Functional Analysis

  • Banach Space
  • Functional Analysis

  • Classroom Articles on Analysis (Up to College Level)

  • Analysis
  • Convolution
  • Bernoulli Number
  • Delta Function
  • Calculus of Variations
  • Fourier Series
  • Cantor Set
  • Gamma Function