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.
Lecture Video and Summary
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Diagonalization and Powers of A (00:51:50)
Lecture 22: Diagonalization and Powers of A
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- Read Section 6.2 in the 4th or 5th edition.
Problem Solving Video
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Powers of a Matrix (00:09:06)
Problem Solving: Powers of a Matrix
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Problems and Solutions
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