Geodesic
Invariant Neutral Subspaces for Symmetric and Skew Real Matrix Pairs
Canadian journal of mathematics, Tome 46 (1994) no. 3, pp. 602-618

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Real matrix pairs (A,H) satisfying det H ≠ 0, HT = εH, and HA - ηATH, where ε, η take the values +1 or —1, are considered. It is shown that maximal A-invariant H-neutral subspaces have the same dimension (depending on ε and η), called the order of neutrality of the pair (A, H). The order of neutrality of definitizable pairs is investigated. In particular, this concept is used to obtain lower bounds for the number of pure imaginary eigenvalues of low rank perturbations of definitizable pairs when (ε,η) = (1, - 1 ) and when (ε,η) = (—1,—1).
DOI : 10.4153/CJM-1994-032-4
Mots-clés : 15A21, 15A57, indefinite scalar products, matrix pairs, definitizable pairs, invariant subspaces 
Lancaster, P.; Rodman, L. Invariant Neutral Subspaces for Symmetric and Skew Real Matrix Pairs. Canadian journal of mathematics, Tome 46 (1994) no. 3, pp. 602-618. doi: 10.4153/CJM-1994-032-4
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