inner product space
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real or complex vector space with an additional structure called an inner product
~40 min read
Encyclopedic overview
Geometric interpretation of the angle between two vectors defined using an inner product Scalar product spaces, over any field, have "scalar products" that are symmetrical and linear in the first argument. Hermitian product spaces are restricted to the field of complex numbers and have "Hermitian products" that are conjugate-symmetrical and linear in the first argument. Inner product spaces may be defined over any field, having "inner products" that are linear in the first argument, conjugate-symmetrical, and positive-definite. Unlike inner products, scalar products and Hermitian products need not be positive-definite.
In mathematics, an inner product space is a real or complex vector space endowed with an operation called an inner product. The inner product of two vectors in the space is a scalar, often denoted with angle brackets such as in
Excerpted from Wikipedia’s “inner product space” article, available under the CC BY-SA 4.0 licence.