The Eigenvalue Problem For Symmetric Matrices
Heinz Rutishauser · Birkhäuser Boston eBooks · 1990
Matrix eigenvalue problems arise, for example, from Hamilton’s principle; the latter states: A mechanical system whose kinetic and potential energy are given by (1) $$T = \sum\limits_{i = 1}^n {} \sum\limits_{j = 1}^n {} {P_i}_j({q_1},...,{q_n}){\dot q_i}{\dot q_j},\,\,\,\,U = U({q_1},...,{q_n})$$ , evolves between the time instances t0 and t1 in such a way that the functions q i (t) describing the motion make the action integral $$J = \int_{{t_0}}^{{t_1}} {} (T - U)dt$$ stationary, the values q i (t 0 ) 2nd qi(t 1) being held fixed.