---
tag: 0DTCBCKEJP
kind: concept
name: Transvection
aliases: [shear-matrix]
msc: [15A23]
sources:
  - url: https://en.wikipedia.org/wiki/Shear_mapping
    locator: lead section
---

## Summary

A transvection is a linear map, or a matrix, of the form $I + cE_{ij}$ with $i \ne j$, that adds a multiple of one coordinate to another.
Geometrically it is a shear.