Linear Algebra 6.1 Introduction to Linear Transformations

This educational video introduces linear transformations, defining them as functions between vector spaces that satisfy specific properties. It covers terminology like image of a function and preimage, and demonstrates how to verify if a function is a linear transformation. The content also explores matrix transformation and how to apply them to vectors.

Video Chapters:
0:00 Introduction
0:09 A Function Mapping
1:37 More Terminology
2:48 Examples from R2 to R2
5:35 Definition of a Linear Transformation
6:45 Verifying a Linear Transformation
10:41 Verifying a Linear Transformation (on your own)
11:26 Properties of Linear Transformations
12:27 Linear Transformations Given by a Matrix
14:17 Common Linear Transformations
14:48 Applying a Linear Transformation (rotation)
17:27 Up Next
Textbook: Elementary Linear Algebra 8e, Ron Larson

Slide Decks: https://bellevueuniversity-my.sharepoint.com/:f:/g/personal/kbrehm_bellevue_edu/IgDVnTt2BohsRLsMfseN5FijAXYDd49YlIkHeq5cfmCxG2g?e=ZwTt3c

Playlist: https://youtube.com/playlist?list=PLl-gb0E4MII1RjTV2GegmXFTJwTrek8OI&si=g3Xc3yHB5GkmxMF4