Abstract
Let A and B be n× n Hermitian matrices. The matrix pair ( A, B) is called definite pair and the corresponding eigenvalue problem β Ax = α Bx is definite if c( A, B) ≡ inf ‖ x‖= 1 {| H ( A+ iB) x|} > 0. In this note we develop a uniform upper bound for differences of corresponding eigenvalues of two definite pairs and so improve a result which is obtained by G.W. Stewart [2]. Moreover, we prove that this upper bound is a projective metric in the set of n × n definite pairs.
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