Symmetric Matrix Eigenvalue Problems
|Find λ for which nontrivial solutions of Ax = λx exist.|
The standard form of the matrix eigenvalue problem is
where A is a given n × n matrix. The problem is to find the scalar λ and the vector x. Rewriting Eq. (9.1) in the form
it becomes apparent that we are dealing with a system of n homogeneous equations. An obvious solution is the trivial one x = 0. A nontrivial solution can exist only if the determinant of the coefficient matrix vanishes; that is, if ...