Eigenvectors and Eigenvalues of a Matrix | Linear Algebra

A thorough intro to eigenvectors, eigenvalues, and the characteristic equation and characteristic polynomial of a matrix. We define these terms and do many examples, including eigenvalues and eigenvectors of a 3x3 matrix in addition to several 2x2 examples. We'll go over how to find the eigenvalues of a matrix and how to use those to find the eigenvectors of a matrix. We'll finish with a complex eigenvalue example.

Linear Algebra course:    • Linear Algebra  
Linear Algebra exercises:    • Linear Algebra Exercises  

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0:00 Intro
0:24 Definition of Eigenvalue and Eigenvector
2:01 Eigenvectors are Nonzero
2:26 Geometric View of Eigenvalues
4:03 How to Verify x is an Eigenvector
5:38 Deriving the Characteristic Equation
8:27 Example of Characteristic Equation
9:10 Use Characteristic Equation to Find Eigenvalues
11:01 Characteristic Polynomial
12:20 Find Eigenvalues of a 3x3 Matrix
13:34 Eigenvectors of a 3x3 Matrix
16:24 Equivalent Eigenvalue Statements
17:25 Complex Eigenvalues
19:34 Conclusion

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