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pivoxa15
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Homework Statement
Consider T:V->V
where the basis vectors in V are {v1, v2}
So
T(v1) = a(v1) + b(v2)
T(v2) = c(v1) + d(v2)
With T = the square matrix
a c
b d
Now let v1=(1,1) v2=(1,-1)
T(1,1)=1(1,1)+1(1,-1)=(2,0)
T(1,-1)=2(1,1)+1(1,-1)=(3,1)
So T= the squre matrix
1 2
1 1
But T(1,1)=(3,2) which does not equal (2,0)
T(1,-1)=(-1,0) which does not equal (3,1)
The theory does not fit this simple example! What has gone wrong?
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