Lecture 15: Introduction to Linear Transformations (Nicholson Section 2.6)
Sub Project: Linear Algebra Lecture Videos
Alternate Video Access via MyMedia | Video Duration: 13:38
Description: If T_A is a matrix transformation from R^2 to R^2 and I tell you what T_A does to the vector [1;0] and what it does to the vector [0;1] can you use this to figure out what T_A does to any vector x = [x1;x2] in R^2?
6:00 --- how matrix transformations act on the sum of two vectors, how matrix transformations act on the scalar multiple of a vector.
7:45 --- I define “linear transformation” (aka “linear mapping”). Example of a transformation from R^2 to R^2 which is not a linear transformation. Here's a nice video on Linear Transformations and how to present linear transformations using matrices (i.e. as a matrix transformation) by 3Blue1Brown. It’s really worth watching even if we can’t present the graphics this way in class, in the book, or on the exams…
