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Orthogonal Transformation and condition

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eoghan
#1
Dec31-08, 09:31 AM
P: 181
Hi there!
In order to proof the orthogonal condition aijaik=[tex]\delta_{jk}[/tex] j,k=1,2,3
I write the invariance of the length of a vector in two coordinate systems:
x'ix'i=xixi
Using the linear transformation:
x'i=ai1xi1+ai2xi2+ai3xi3
the first term becomes:
aijaikxjxk

My question is: why can't I write
aij2=xj2
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