2B18-19 Principal Values and Principal Directions of Real Symmetric Tensors

Recall the definition that is a linear transformation, transforming into . Let us suppose that and are such that,

  for every

       all in

However, if the vector  is transformed parallel to itself, then

    is called an Eigen vector, and

    is the corresponding Eigen value.

For the special case of   being a unit vector, it is then transformed into a vector parallel to itself.

Let  be a unit eigen vector, then

or  with              

Let

Then,

2B18-19 contd.