Matrix eigenvalues by numerical integration.
David James Shippy · AIAA Journal · 1969
where X is an eigenvalue and I is the unit matrix. As is well known, there are n values of X for which nontrivial solutions (eigenvectors) x of Eq. (1) exist. One component of each eigenvector may be chosen arbitrarily. Let the first component of x be chosen arbitrarily and designated as xi*. Then, following the procedure of Kane, consider X and the other n — 1 components Xi to be functions of a variable r. Designate x and X at r — 0 as x and X, respectively. Define a constant vector c by the relation