## Quick Reference

A square of side 1 unit. Specifically the unit square defined by *O* (0, 0), *I* (1, 0), *K* (1, 1), *J* (0, 1) is of interest in matrix transformations in the plane. It can be used to identify the transformation from a matrix, or find the matrix if the transformation is known because the images of points *I* and *J* form the columns of the matrix which performs that transformation. For example, in a rotation of 90° clockwise (about the origin), the image of *I* is (0, −1) and the image of *J* is (1, 0) so the matrix is . If a matrix of a transformation is then the image of *I* is just the first column, i.e. (1, 0), so it has not moved, and the image of *J* is (3, 1), so the transformation is a shear parallel to the *x*-axis which moves (0, 1) to (3, 1).

*Subjects:*
Mathematics.

## Related content in Oxford Index

##### Reference entries

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.