12-240/Classnotes for Tuesday October 23: Difference between revisions

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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

== Lecture notes scanned by [[User:Zetalda|Zetalda]] ==
== Lecture notes scanned by [[User:Zetalda|Zetalda]] ==
<gallery>
<gallery>

Revision as of 15:20, 30 October 2012

=

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

Lecture notes scanned by Zetalda