Linear Algebra 7.1 Eigenvalues and Eigenvectors

Video Chapters:
This educational video provides a comprehensive introduction to eigenvectors, eigenvalues, and eigenspaces within the context of linear algebra. The lesson begins by defining an eigenvector as a non-zero vector that, when multiplied by a square matrix, results in a simple scalar multiple of itself. Viewers will learn how to verify if a given vector is an eigenvector and how to determine its corresponding eigenvalue.

The tutorial also covers the reverse process: determining whether a given scalar is an eigenvalue and, if so, finding the associated eigenvectors through algebraic manipulation and row reduction. Finally, the video explores the concept of an eigenspace, demonstrating how these vectors form a subspace that includes the zero vector and can be represented parametrically.

Video Chapters:
00:00 Intro
00:10 Eigenvalues and Eigenvectors
01:30 Determine an Eigenvalue
02:13 Verify an Eigenvalue
04:18 Verify an Eigenvalue and Find an Eigenvector
06:51 Eigenspace
07:43 Find a Basis for the Eigenspace in R3
09:49 The Characteristic Equation/Polynomial
10:42 Determine Eigenvalue(s) Example 1
12:28 Determine Eigenvalue(s) Example 2
13:42 Determine Eigenvalue(s) and Eigenvectors
17:40 Determine Eigenvalues in R3
19:48 Determine Eigenvalues in R4
22:05 Determine Eigenvalues Given the Characteristic Polynomial
23:26 Linear Transformations (rejoice!!)
27:50 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