# Inner Product Spaces--A Primer

DevFeed: [Inner Product Spaces--A Primer](<https://devfeed.tech/articles/inner-product-spaces-a-primer-40231.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2011/07/25/inner-product-spaces-a-primer/>)

Published: 2011-07-25T00:29:00Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Mathematics](<https://devfeed.tech/topics/mathematics.md>), [Math and Logic](<https://devfeed.tech/topics/math-and-logic.md>), [Computing](<https://devfeed.tech/topics/computing.md>)

Tags: [big-o-notation](<https://devfeed.tech/tags/big-o-notation.md>), [eigenvectors](<https://devfeed.tech/tags/eigenvectors.md>), [inner-product](<https://devfeed.tech/tags/inner-product.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [matrices](<https://devfeed.tech/tags/matrices.md>), [orthogonality](<https://devfeed.tech/tags/orthogonality.md>), [symmetry](<https://devfeed.tech/tags/symmetry.md>), [vector-spaces](<https://devfeed.tech/tags/vector-spaces.md>), [vectors](<https://devfeed.tech/tags/vectors.md>)

## AI overview

This primer explains why vector spaces can be extended with a dot-product-like operation and defines inner products through conjugate symmetry, linearity, additivity, and positive definiteness. It introduces inner product spaces and discusses their connection to linear functionals.

## Source excerpt

Vector spaces alone are not enough to do a lot of the interesting things we'd like them to do. Since a vector space is a generalization of Euclidean space, it is natural for us to investigate more specific types of vector spaces which are more akin to Euclidean space. In particular, we want to include the notion of a dot product. By admitting additional structure to a vector space, we may perform more computations, and hopefully get more interesting results.