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# Lecture19 - University of Toronto at Scarborough Department...

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University of Toronto at Scarborough Department of Computer & Mathematical Sciences MAT A23 Winter 2008 Lecture 19 Eigenvalues and Eigenvectors Sophie Chrysostomou definition 0.1 Let A be an n × n matrix. A scalar λ is an eigenvalue of A if there is a nonzero vector v R n , such that A v = λ v . In this case, v is called an eigenvector of A corresponding to the eigenvalue λ . How to Find the Eigenvalues of a Square Matrix definition 0.2 Let A be an n × n matrix. The characteristic polynomial of A is given by p ( λ ) = | A - λI | . If λ is an eigenvalue of A , then the set E λ = { x A x = λ x } is called the eigenspace of λ . It contains the zero vector and all the eigenvec-

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Lecture19 - University of Toronto at Scarborough Department...

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