12-240/Classnotes for Tuesday October 23: Difference between revisions
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Revision as of 17:00, 30 October 2012
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Definition: L(V,W) is the set of all linear transformation L: V->W
u [math]\displaystyle{ \in\,\! }[/math] V, 0 of L(V,W) (u)=0 of W (this is a l.t.str)
If L1 and L2 [math]\displaystyle{ \in\,\! }[/math] L(V,W), (L1 + L2) (u)= L1(u) +L2(u) (this is a l.t.str)
If c [math]\displaystyle{ \in\,\! }[/math] F and L [math]\displaystyle{ \in\,\! }[/math] L(V,W), (c*L) (u)= c*L(u) (this is a l.t.str)
Theorem: L(V,W) is a vector space
Proof: "Distributivity" c(x+y)=cx+cy
In our case need to show c(L1 + L2)= cL1 + cL2
Where c [math]\displaystyle{ \in\,\! }[/math] F and L1 and L2 [math]\displaystyle{ \in\,\! }[/math] L(V,W)
(LHS) (u)
Lecture notes scanned by Zetalda
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