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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[@WrathofMath]

Help me keep producing this course and access the lecture notes and exclusive videos by joining Wrath of Math! kzbin.info/door/yEKvaxi8mt9FMc62MHcliwjoin Watch the rest of the course: Linear Algebra course: kzbin.info/aero/PLztBpqftvzxWT5z53AxSqkSaWDhAeToDG Linear Algebra exercises: kzbin.info/aero/PLztBpqftvzxVmiiFW7KtPwBpnHNkTVeJc

[@SILE75]

You're the reason why I pass Linear Algebra and Introductory Analysis. Thank you for all your videos

[@WrathofMath]

So glad to help! Thank you for watching!

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[@WrathofMath]

Thank you so much, glad my content has been helpful for you!

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Saving the exam, continue the great work!!!!

[@WrathofMath]

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[@WrathofMath]

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[@WrathofMath]

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[@artiologist-ifrah9138]

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[@spectrumwenly2171]

10:57 why do we already know -1 is one of the eigenvalues?

[@WrathofMath]

Just because it was part of an example we did earlier in the video when verifying an eigenvector!

[@spectrumwenly2171]

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