LA57 How To Find Eigenvalues and Eigenvectors?

Eigenvalues & Eigenvectors, characteristic polynomial, eigenspaces, and the reasoning behind the common method used for finding eigenvalues and eigenvectors of small matrices. A detailed example illustrates the method and its connection to diagonalization of matrices. Subscribe @Shahriari for more undergraduate Math vidoes.
00:00 Introduction
00:16 Definition: Eigenvectors & Eigenvalues for Matrices (LA56 Eigenvectors & Eigenvalues for L...)
01:25 Definition: Eigenvectors & Eigenvalues for Linear Operators
02:21 Using Matrices to find Eigenvectors & Eigenvalues for Linear Operators
03:45 Characterizations of Eigenvectors & Eigenvalues, the argument
11:05  Characterizations of Eigenvectors & Eigenvalues, the Theorem
11:55 Eigenvectors & Eigenvectors over general Fields
12:22 Definition: Characteristic Polynomial (LA58 The Characteristic Polynomial of...)
12:40 Definition: Eigenspaces (LA60 Eigenspaces, Diagonalization, an...)
13:20 Example: Finding Eigenvalues of a 2x2 matrix
16:27 Example Continued: Finding Eigenvectors
19:23 Example Continued: Geometric illustration of eigenvalues & eigenvectors
21:36 Example Continued: A basis of Eigenvectors & Diagonalization (LA59 Diagonalizability of matrices an...)
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This is a video in a series of lectures on linear algebra. The series is a rigorous treatment meant for students with no prior exposure to linear algebra. In this full undergraduate course in linear algebra, general vector spaces and linear transformations are emphasized.

Shahriar Shahriari is the William Polk Russell Professor of Mathematics at Pomona College in Claremont, CA USA
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