Class 7
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Examples in file
eigexamples1.m;
(see also the
applet)
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examples for 2 by 2 matrices, triangular, complex conjugate pair:
(i) that have 2 lin. indep. eigenvectors and
(ii) that have only 1 lin. indep. eigenvector
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Example: If lambda is an eigenvalue of A, then lambda^n is an eigenvalue
of A^n (^n denotes power) - with proof.
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Theorem 1: The eigenvalues of a triangular matrix are the entries on its
main diagonal (with proof).
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Theorem 2: (r distinct eigenvalues implies r lin. indep. eigenvectors)
with proof - done carefully.
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though not done yet - please see:
characteristic equation/polynomial (definitions/examples)