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G R a D U a T E 2 0 0 2 0 3 a PManualzz  Form

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cool so last time we introduced our main theorem which is our Jordan decomposition so if you have any Matrix a so theorem this is my Jordan decomposition given any complex Matrix Square Matrix complex Square Matrix we can write a as well some change of basis and then instead of a diagonal matrix it's nice when you can diagonalize and some Matrix you can diagonalize but as you saw last time you can't always diagonalize so this is kind of the next best thing where we say well we can get an almost diagonal matrix where that almost diagonal matrix is called J where J is some Matrix made up of these Jordan blocks so some first block of size K1 with entries Lambda 1 down through some final Jordan block of size km with in Lambda M where each block each let's say j k of Lambda is a k byk Matrix with lambdas along the diagonal and ones directly above the lambdas and Zer everywhere else where this is a k byk Matrix [Applause] and we said and we saw it last time actually t

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