2B18 (f) : Example revisited

Let us revisit the previous example problem where we found the eigen values and eigen vectors for a given tensor.

The above is in x,y,z coordinate system. Note the vectors on y and z planes are not normal. Now after the determinate of the eigen values and corresponding eigen vectors,

          

Note that the new orientations coincide with the eigen vectors; and the eigen values have zero in non-normal  directions