12-240/Classnotes for Tuesday October 23: Difference between revisions
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== === |
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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, |
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0 of L(V,W) (u)=0 of W (this is a l.t.str) |
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If L1 and L2 <math>\in\,\!</math> L(V,W), |
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(L1 + L2) (u)= L1(u) +L2(u) (this is a l.t.str) |
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If c <math>\in\,\!</math> F and L <math>\in\,\!</math> L(V,W), |
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(c*L) (u)= c*L(u) (this is a l.t.str) |
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Theorem: L(V,W) is a vector space |
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== Lecture notes scanned by [[User:Zetalda|Zetalda]] == |
== Lecture notes scanned by [[User:Zetalda|Zetalda]] == |
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<gallery> |
<gallery> |
Revision as of 14:20, 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