# Lecture20 - 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 20 Diagonalizable Matrices Sophie Chrysostomou definition 0.1 Let A and D be an n × n matrices. a) D is a diagonal matrix , if all its entries not on the main diagonal are zero. ie. d ij = 0 for all i = j . b) A is diagonalizable if there exists an invertible n × n matrix P such that P - 1 AP is a diagonal matrix. theorem 0.2 Let A be an n × n matrix. A is diagonalizable ⇐⇒ A has n linearly independent eigenvectors. 1

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theorem 0.3 Let v 1 , v 2 , · · · , v

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