Laguerre’s method applied to the matrix eigenvalue problem

Introduction. We present a new algorithm for the calculation of the eigenvalues of real square matrices of orders up to 100. The basic method is directly applicable to complex matrices as well and, in both cases, with each eigenvalue X of A a vector v is produced for which (A -XI)v is null except for a small last element. This vector is not always an approximation to the eigenvector for X and this algorithm claims only to find eigenvalues.