Difference between revisions of "12-240/Classnotes for Tuesday October 23"
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Definition: L(V,W) is the set of all linear transformation L: V->W | Definition: L(V,W) is the set of all linear transformation L: V->W | ||
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+ | u <math>\in\,\!</math> V, | ||
+ | 0 of L(V,W) (u)=0 of W (this is a l.t.str) | ||
+ | |||
+ | If L1 and L2 <math>\in\,\!</math> L(V,W), | ||
+ | (L1 + L2) (u)= L1(u) +L2(u) (this is a l.t.str) | ||
+ | |||
+ | If c <math>\in\,\!</math> F and L <math>\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 | ||
+ | |||
== Lecture notes scanned by [[User:Zetalda|Zetalda]] == | == Lecture notes scanned by [[User:Zetalda|Zetalda]] == | ||
<gallery> | <gallery> |
Revision as of 15:20, 30 October 2012
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Definition: L(V,W) is the set of all linear transformation L: V->W
u V, 0 of L(V,W) (u)=0 of W (this is a l.t.str)
If L1 and L2 L(V,W), (L1 + L2) (u)= L1(u) +L2(u) (this is a l.t.str)
If c F and L L(V,W), (c*L) (u)= c*L(u) (this is a l.t.str)
Theorem: L(V,W) is a vector space