Hi there! In order to proof the orthogonal condition a_{ij}a_{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'_{i}x'_{i}=x_{i}x_{i} Using the linear transformation: x'_{i}=a_{i1}x_{i1}+a_{i2}x_{i2}+a_{i3}x_{i3} the first term becomes: a_{ij}a_{ik}x_{j}x_{k} My question is: why can't I write a_{ij}^{2}=x_{j}^{2}