# Linear Transformations - Outline * DS Mental Model Principle * *Relationships* between spaces * **Linear Transformations** * may need to go in another post, but not sure. * Linear Algebra Goodnotes pg 5,6,7 * A Geometrical Understanding of Matrices (Goodnotes) * Ways to view a matrix (notability) * Note: fascinating that a matrix has rows and columns, so clearly there is some relationship. That can be thought of as the four fundamental subspaces * Change of basis * Four fundamental subspaces & transpose (notability note, pg 9, whiteboard note) * Change of basis, notability, eli b * Data and Linear regression perspective (notability, ways to view a matrix) * this gets us to notion of closeness. Makes sense when vectors are arrows (line segments), but highlight how this can occur when they are other things, all isomorphic to Rn * Domain, codomain, etc, types of maps (injective, surjective) * Ways to interpret matrix: * [Dear linear algebra students, This is what matrices (and matrix manipulation) really look like - YouTube](https://www.youtube.com/watch?v=4csuTO7UTMo&t=100s) * Linear maps and matrices are the same object, just different representations (see pg 155 Jkun text) * A vector, say [2, 1] wrt e1 and e2 (canonical) basis, will still be [2,1] *after* a linear transformation $A$, but it will now be described wrt *where e1 and e2 landed *! ([What is Jacobian? | The right way of thinking derivatives and integrals - YouTube](https://youtu.be/wCZ1VEmVjVo?list=PLwcClAaLqrJyzeqgdc9dJYRh9OYawfkSL&t=166)) --- Date: 20220612 Links to: Tags: #review References: * []()