10. Eigenvalue Bounds
Beresford Ν. Parlett · Society for Industrial and Applied Mathematics eBooks · 1998
Useful information about the eigenvalues of A may be obtained from some of its submatrices. In addition A's eigenvalues can be related to those of neighboring matrices in a way that goes far beyond standard perturbation theory (the effect of small changes). Such investigations began in the nineteenth century and continue to this day. Much recent work extends the matrix theory to cover differential and integral operators.