In flight, interactions between aerodynamic forces and a flexing airframe induce vibrations. When an airplane flies at a speed greater than a certain threshold, those self-excited vibrations become unstable, leading to flutter. Engineers had to use certain differential equations to estimate the flutter speed and this process led to finding the eigenvalues of a square matrix. Eigenvalues are useful in geometry when dealing with R 3 space and vectors along a line given by l x . They can be determined algebraically also.
Eigenvalues are useful in dynamical systems as well.
Olga used them to help find the vibrations that interactions between aerodynamic forces and a flexing airframe induce. This was a very time consuming task. Olga found a way to reduce the amount of calculation. She wanted to refine a method for getting useful information about the eigenvalues without having to go to all the extra trouble involved in computing them exactly. This theorem deals with a square matrix that has entries that can be complex numbers.