Orthogonalising nearly orthogonal axis sets

If data for a symmetrical tensor, or ellipsoid, are reported in terms of principal axis values and axis directions, where the latter, through rounding, do not adequately reflect the orthogonality of the principal axes, the reconstructed reference-axis tensor will not adequately represent the original tensor. An analytical solution for axis adjustment is given and is compared with a previous empirical method. If principal axis directions were specified in terms of the strike and dip of a plane containing two of the axes, and the pitch of one of those axes within it, the problem would not arise.