# Exercise 725 for each linear operator t find a jordan

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Exercise 7.2.5 : For each linear operator T , find a Jordan canonical form J of T and a Jordan canonical basis β for T . (b) T is the linear operator on P 3 ( R ) defined by T ( f ( x ) ) = xf 00 ( x ) .
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so we can just take w = 1. Thus the Jordan canonical form of T is J = 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 , and a Jordan canonical basis is β = { 12 x, 6 x 2 , x 3 , 1 } . (e) T is the linear operator on M 2 × 2 ( R ) defined by T( A ) = 3 1 0 3 · ( A - A t ) .