@Article{JCM-9-3,
author = {Sun, Ji-Guang},
title = {Rayleigh Quotient and Residual of a Definite Pair},
journal = {Journal of Computational Mathematics},
year = {1991},
volume = {9},
number = {3},
pages = {247--255},
abstract = {<p style="text-align: justify;">Let {$A,B$} be a definite matrix pair of order $n$, and let $Z$ be an $l$-dimensional subspace of $C^n$. In this paper we introduce the Rayleigh quotient matrix pair&nbsp;<br/>{$H_1,K_1$} and residual matrix pair&nbsp; {$R_A,R_B$} of {A,B} with respect to Z, and used the norm of {$R_A,R_B$} to bound the difference between the eigenvalues of {$H_1,K_1$} and that of {$A,B$}, and to bound the difference between $Z$ and an $l$-dimensional eigenspace of {$A,B$}. The corresponding classical theorems on the Hermitian matrices can be derived from the results of this paper.</p>},
issn = {1991-7139},
doi = {https://doi.org/1991-JCM-9398},
url = {https://global-sci.com/article/86004/rayleigh-quotient-and-residual-of-a-definite-pair}
}