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 textbook.

Problem Solving Video

  • Watch the recitation video on Eigenvalues and Eigenvectors (00:09:21)
  • Recitation video transcript (PDF)

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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