Lecture 11: Matrix Transformations (Nicholson Section 2.2)
Sub Project: Linear Algebra Lecture Videos
Alternate Video Access via MyMedia | Video Duration: 28:32
Description: Warning: the lectures came from a book that referred to “matrix mappings”, “linear mappings”, and “linear operators”. Nicholson’s book refers to “matrix transformations”, “linear transformations” and “geometrical transformations”. So whenever I say the word “mapping” you should think “transformation”. Started matrix mappings w/ a review of language from high school: function, domain, range, etc. Introduced language of “codomain”.
6:55 --- given an mxn matrix A, define the matrix transformation (aka matrix mapping) T_A (aka f_A).
12:50 --- Did two examples of matrix transformations where the matrices A are both 2x2 matrices.
15:30 --- Showed how to represent the matrix transformation graphically via “before” and “after pictures”. Note that from the graphic representation it’s clear that T_A(x+y) = T_A(x) + T_A(y).
21:00 --- For the first example, does it appear that the matrix mapping is onto R^2?
21:35 --- Did second example, discussing its graphic representation. It’s clearly not going to be onto R^2.
