Orthogonal Transformation and condition

eoghan

Hi there!
In order to proof the orthogonal condition a_ija_ik=[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=x_ix_i
Using the linear transformation:
x'_i=a_i1x_i1+a_i2x_i2+a_i3x_i3
the first term becomes:
a_ija_ikx_jx_k

My question is: why can't I write
a_ij²=x_j²