Difference between revisions of "12-240/Classnotes for Tuesday September 25"

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(Definition)
(Definition)
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Then, (+): VxV->V is (v,w)= v+w; (.): FxV->V is (c,v)=cv
 
Then, (+): VxV->V is (v,w)= v+w; (.): FxV->V is (c,v)=cv
 +
 +
Such that
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 +
VS1 <math>\forall\!\,</math> x, y <math>\in\!\,</math> V: x+y = y+x
 +
 +
VS2
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VS3
 +
VS4
 +
VS5
 +
VS6
  
 
==Scanned Notes by [[User:Richardm|Richardm]]==
 
==Scanned Notes by [[User:Richardm|Richardm]]==

Revision as of 19:34, 25 September 2012

Today's class dealt with the properties of vector spaces.


Definition

Let F is a field, a vector space V over F is a set V of vectors with special element O ( of V) and tow operations: (+): VxV->V, (.): FxV->V

VxV={(v,w): v,w \in\!\, V}

FxV={(c,v): c \in\!\, F, v \in\!\, V}

Then, (+): VxV->V is (v,w)= v+w; (.): FxV->V is (c,v)=cv

Such that

VS1 \forall\!\, x, y \in\!\, V: x+y = y+x

VS2 VS3 VS4 VS5 VS6

Scanned Notes by Richardm