how can we solve this type problems we dont want specific solution. we want to use as A input everytime different matrix. three axis have each rotation degree

symmetric second-order tensor. Such axes are called the principal axes of the tensor. For this case, the basis vectors are actually the unit principal directions l"i". nan, nay. and it can be shown that with respect to principal axes the tensor reduces to the diagonal form Note that the fundamental invariants defined by relations (1.6.3) can be expressed in terms of the principal values as The eigenvalues have important extremal properties. If we arbitrarily rank the priacipal values such that > a2 > as, then 1 will be the largest of all possible diagonal elemen(s. smallest diagonal element possible. This theory is applied in elasticity as yeyock the largest stress o strain components in an elastic solid. 3 will be th EXAMPLE 1.3: PRINCIPAL VALUE PROBLEM Determine the invariants and principal values and directions of the following symmetric second- order tensor 2 0 0 04-3 The invariants follow from relations (1.6.3) 6-25-625 03 14-310 -3 lll-lo 3-41-2(-9-16)--50 4-3 0 The characteristic equation then becomes (2-2) (F-25) 0 Thus, for this case all principal values are distinct