9

Symmetric Matrix Eigenvalue Problems

Find λ for which nontrivial solutions of Ax = λx exist. |

The standard form of the matrix eigenvalue problem is

(9.1) |

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

(9.2) |

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 ...

Start Free Trial

No credit card required