MAS 801 It's a Discreetly Discrete World – Mathematics in Real-life ...
MAS 801 It's a Discreetly Discrete World – Mathematics in Real-life ...
MAS 801 It's a Discreetly Discrete World – Mathematics in Real-life ...
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Lecture 9: 22 October 2008<br />
Eigenvalues & Eigenvectors<br />
• How do we f<strong>in</strong>d eigenvectors correspond<strong>in</strong>g to eigenvalues<br />
• This is more difficult than f<strong>in</strong>d<strong>in</strong>g eigenvalues<br />
• Eigenvectors are not unique<br />
• For A = 3 1 , any vector of the form k (k ≠ 0) is an<br />
1 3<br />
k<br />
eigenvector correspond<strong>in</strong>g to the eigenvalue 4<br />
• Check!<br />
• If x is an eigenvector of A, so is kx for every k ≠ 0<br />
• To f<strong>in</strong>d eigenvectors, we must solve systems of l<strong>in</strong>ear equations
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