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Relating the spectrum of a matrix and a principal submatrix using adjugates and Schur complements | | M. Thüne
; | | Date: |
5 Sep 2016 | | Abstract: | Given an annihilating polynomial for a matrix or one of its principal
submatrices, one can relate the eigensolutions of both matrices by deriving an
adjugate and using the method of Schur complements. Generalizable to matrices
over $mathbb{C}left[lambda
ight]$, the technique may be employed on
polynomial eigenvalue problems. It is particular useful for practical
eigenvalue computations when the matrix sizes are close to each other and the
degree of the annihilating polynomial is low. An application to the spectrum of
a perturbed strongly regular graph is considered. | | Source: | arXiv, 1609.1089 | | Services: | Forum | Review | PDF | Favorites | |
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