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 | ||
+ | |||
+ | 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 | ||
+ | |||
+ | Proof: "Distributivity" c(x+y)=cx+cy | ||
+ | |||
+ | In our case need to show c(L1 + L2)= cL1 + cL2 | ||
+ | |||
+ | Where c <math>\in\,\!</math> F and L1 and L2 <math>\in\,\!</math> L(V,W) | ||
+ | |||
+ | (LHS) (u) | ||
+ | |||
== Lecture notes scanned by [[User:Zetalda|Zetalda]] == | == Lecture notes scanned by [[User:Zetalda|Zetalda]] == | ||
<gallery> | <gallery> | ||
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Image:12-240-Oct23-3.jpeg|Page 3 | Image:12-240-Oct23-3.jpeg|Page 3 | ||
Image:12-240-Oct23-4.jpeg|Page 4 | Image:12-240-Oct23-4.jpeg|Page 4 | ||
+ | </gallery> | ||
+ | |||
+ | == Lecture notes scanned by [[User:KJMorenz|KJMorenz]] == | ||
+ | <gallery> | ||
+ | Image:12-240-Oct30.jpg|Oct 30 Page 1 | ||
+ | Image:12-240-Oct30-2.jpg|Oct 30 Page 2 | ||
+ | Image:12-240-Oct2.jpg|Oct 2 Page 1 | ||
+ | Image:12-240-Oct2-2.jpg|Oct 2 Page 2 | ||
+ | Image:12-240-Oct2-3.jpg|Oct 2 Page 3 | ||
+ | Image:12-240-Oct2-4.jpg|Oct 2 Page 4 | ||
+ | Image:12-240-Basis.jpg|Basis of a Vector Space | ||
+ | Image:12-240-TutOct4.jpg|Tutorial Oct 4 | ||
</gallery> | </gallery> |
Latest revision as of 07:37, 22 October 2014
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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
Proof: "Distributivity" c(x+y)=cx+cy
In our case need to show c(L1 + L2)= cL1 + cL2
Where c F and L1 and L2 L(V,W)
(LHS) (u)