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,
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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]] ==
 
<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 \in\,\! V, 0 of L(V,W) (u)=0 of W (this is a l.t.str)

If L1 and L2 \in\,\! L(V,W), (L1 + L2) (u)= L1(u) +L2(u) (this is a l.t.str)

If c \in\,\! F and L \in\,\! 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 Zetalda