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Diagonalization and Powers of A

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Session Overview

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

If A has n independent eigenvectors, we can write A = SΛS−1, where Λ is a diagonal matrix containing the eigenvalues of A. This allows us to easily compute powers of A which in turn allows us to solve difference equations uk+1 = Auk.

Session Activities

Lecture Video and Summary

  • Watch the video lecture Diagonalization and Powers of A (00:51:50)
  • Read the accompanying lecture summary (PDF)
  • Lecture video transcript (PDF)

Suggested Reading

  • Read Section 6.2 in the textbook.

Problem Solving Video

  • Watch the recitation video on Powers of a Matrix (00:09:06)
  • Recitation video transcript (PDF)

Check Yourself

Problems and Solutions

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

 

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