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

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

Proof: "Distributivity" c(x+y)=cx+cy

In our case need to show c(L1 + L2)= cL1 + cL2

Where c \in\,\! F and L1 and L2 \in\,\! L(V,W)

(LHS) (u)

Lecture notes scanned by Zetalda

Lecture notes scanned by KJMorenz