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Unformatted text preview: x;y 2 V and T.˛x/ D ˛T.x/ for all ˛ 2 K and x 2 V . An endomorphism of a vector space V is a linear transformation T W V ! V . The kernel of linear transformation T W V ! W is f v 2 V W T.v/ D g . The range of T is T.V / . Example 3.3.5. (a) Fix a polynomial f.x/ 2 KŒxŁ . The map g.x/ 7! f.x/g.x/ is a linear transformation from KŒxŁ into KŒxŁ . (b) The formal derivative P k ˛ k x k 7! P k k˛ k x k ± 1 is a linear transformation from KŒxŁ into KŒxŁ . (c) Let V denote the complex vector space of C –valued continuous functions on the interval Œ0;1Ł . The map f 7! f.1=2/ is a linear transformation from V to C ....
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This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.
 Fall '08
 EVERAGE
 Algebra, Vector Space

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