Incoming links: Metric induced by a norm
Metric (mathematics) Updated 2025-07-16
A metric is a function that give the distance, i.e. a real number, between any two elements of a space.
Because a norm can be induced by an inner product, and the inner product given by the matrix representation of a positive definite symmetric bilinear form, in simple cases metrics can also be represented by a matrix.
Metric space vs normed vector space vs inner product space Updated 2025-07-16
TODO examples:
- metric space that is not a normed vector space
- norm vs metric: a norm gives size of one element. A metric is the distance between two elements. Given a norm in a space with subtraction, we can obtain a distance function: the metric induced by a norm.
Hierarchy of topological, metric, normed and inner product spaces
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