Characteristic Polynomials of Some Perturbed Matrices
Using a determinant identity, we establish an algebraic relation between the characteristic polynomial of a matrix and its perturbation of special structure. When the perturbation satisfies some linear independence condition, the factored expression of the characteristic polynomial of the perturbed matrix is obtained. Some known eigenvalue theorems in the literature can be derived directly as corollaries of the new result. (c) 2007 Elsevier Inc. All rights reserved.
Applied Mathematics and Computation
(2008). Characteristic Polynomials of Some Perturbed Matrices. Applied Mathematics and Computation, 199(2), 631-636.
Available at: http://aquila.usm.edu/fac_pubs/1515