Orthogonal Transformation and condition

1. eoghan

189
Hi there!
In order to proof the orthogonal condition aijaik=$$\delta_{jk}$$ 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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