12-240/Classnotes for Thursday October 18

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Linear transformation

Definition: A function L: V-> W is called a linear transformation if it preserve following structures:

1) L(x + y)= L(x) + L(y) 2) L(cx)= c.L(x) 3) L(0 of V) = 0 of W

Proposition:

1) property 2 leads to property 3 2) L: V -> W is a linear transformation iff [math]\displaystyle{ \forall\,\! }[/math] c [math]\displaystyle{ \in\,\! }[/math], [math]\displaystyle{ \forall\,\! }[/math] x, y [math]\displaystyle{ \in\,\! }[/math] V: L(cx + y)= cL(x) + L(y)

lecture note on oct 18, uploaded by starash