Eigenvalues and Eigenvectors

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Session Overview

Figure excerpted from 'Introduction to Linear Algebra' by G.S. Strang

If the product Ax points in the same direction as the vector x, we say that x is an eigenvector of A. Eigenvalues and eigenvectors describe what happens when a matrix is multiplied by a vector. In this session we learn how to find the eigenvalues and eigenvectors of a matrix.

Session Activities

Lecture Video and Summary

Suggested Reading

  • Read Section 6.1 through 6.2 in the 4th or 5th edition.

Problem Solving Video

Check Yourself

Problems and Solutions

Work the problems on your own and check your answers when you're done.

Further Study

Eigenvalue Demonstrations*

These demonstrations employ Java® applets with voice-over narration by Professor Strang.

Mini-lectures on Eigenvalues

These mini-lectures with voice-over narration below help to explain some key Eigenvalue concepts.

*Funding for these demonstrations was provided by a grant from the The d'Arbeloff Fund for Excellence in MIT Education as part of The d'Arbeloff Interactive Mathematics Project (d'A I M P).


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