Orthogonal Transformation and condition

  1. 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
     
  2. jcsd
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