A geometrical method for diagonalizing real, symmetric 3×3 matrices through Euler rotations

摘要

The classical problem of finding the principal values (eigenvalues) and principal axes (eigenvectors) of a physical property represented by a second-rank symmetric tensor is treated in textbooks by solving the characteristic equation associated with the 3×3 symmetric matrix representation. The same problem is solved here without reference to the characteristic equation. By use of Euler rotations, analytical expressions are attained for the Euler eigenangles, the eigenvalues and the eigenvectors.