---
tag: 0AZ5ARP287
kind: concept
name: Dual map
aliases: [transpose-of-a-linear-map]
msc: [15A04]
sources:
  - url: https://en.wikipedia.org/wiki/Transpose_of_a_linear_map
    locator: Definition
same_as:
  wikidata: Q2858846
  wikipedia: Transpose of a linear map
---

## Summary

The dual map of a linear map $T \colon V \to W$ is the linear map $W^* \to V^*$ that sends each linear form $f$ to $f \circ T$.