ABSTRACT
Equations of the type [A]{x} = λ{x} (4.1)
often occur in practice, for example in the analysis of structural stability or the natural frequencies of vibrating systems. We have to find a vector {x} which, when multiplied by [A], yields a scalar multiple of itself. This multiple λ is called an “eigenvalue” or “characteristic value” of [A] and we shall see there are n of these for a matrix of order n. Physically they might represent frequencies of oscillation. There are also n vectors {x}, one associated with each of the eigenvalues λ. These are called “eigenvectors” or “characteristic vectors” . Physically they might represent the mode shapes of oscillation.
