Example of a linear transformation on R^2: shear

Created almost 9 years ago, updated about 8 hours ago

A horizontal shear is $T(x,y)=(x+ky,y)$ with matrix $\begin{bmatrix}1&k\\0&1\end{bmatrix}$. It fixes the horizontal axis, has determinant one, and preserves area but generally changes lengths and angles. Its inverse uses $-k$.

Parents

Like how this is organised?

Build your own knowledge tree on knowen.md: notes, decisions and tasks in one connected markdown graph, shared with your team and your AI agents.