[Linear Algebra] Eigenvalues and Eigenvectors

In this video I go over the definitions of eigenvalues, eigenvectors, and eigenspaces. We also go over two theorems related to these concepts and many examples.

1:12 Eigenvalues and Eigenvectors Definition
4:16 Example: Finding an Eigenvector Given an Eigenvalue
7:28 Eigenspaces
9:21 Example: Basis of Eigenspace
10:59 Theorem: Eigenvalues of Triangular Matrices
12:44 Theorem: Eigenvectors Corresponding to Distinct Eigenvalues
16:38 Example: Maximum Number of Distinct Eigenvalues
17:50 Example: Finding Eigenvalues Without Calculation
19:29 Example: Eigenvalues When A^2 is the Zero Matrix

The content of this video is based off of chapter 5.1 in Linear Algebra, 4th Edition by David Lay.

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