A characteristic polynomial factorization: extending some matrix eigenvalue estimates
David Foulkes · 1998
For matrices E e G, P e C', J e C, let A = E-PG'^€ C''. PJ-EP E eC {n-t-m)x(n + m) Then the characteristic polynomials of J, A and % are related by pi{z)pA(.z) = p%(z) ■ Eigenvalue estimales for several types of matrices A may be obtained by examining '&. We estimate a) the eigen values of Mondriga (and other) mixed-sign matrices, which arise in the geometry of immobilization as posed by Kuperberg and Papadimitriou, and which motivated this factorization; b) the eigenvalues of non-negative matrices different from the spectral radius; c) the eigenvalues of matrices with one sign on and another off the main diagonal. Also, we show a method for shifting the GerSgorin Disks.