Linear maps preserve the origin, linear combinations, collinearity, and parallel directions (possibly collapsing them). They need not preserve lengths, angles or area. In $\mathbb R^2$, the unit square maps to the parallelogram spanned by $T(e_1),T(e_2)$; singular maps can collapse it to a segment or point.
Parents
Children
- Visualise a linear transformation on R^2 by looking at the image of a regionTo visualize $T(x)=Ax$ on $\mathbb R^2$, transform the vertices and edges of a square or grid. For...
- Geometric properties of linear transformations on R^2For a real $2\times2$ matrix, the column vectors give the images of the coordinate axes. Absolute determinant...
No children match.
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.