Abstract
We start by proving a lower bound for the lp operator norm of a submatrix with sufficiently large dimensions and some relations between the lp norm and the lp operator norm. We then study the lp norm and the lp operator norm of certain matrices arising in estimating the eigenvalue, generalized eigenvalue, singular-value, and generalized singular-value variations of matrices, matrix pencils, and matrix pairs. Finally, as applications of our bounds upon the lp norm and lp operator norm of certain matrices, we give several new bounds for the variations of the spectra of matrices and matrix pencils. These new bounds are generalizations of the Weyl-Lidskii theorem for Hermitian matrices and the Bhatia-Davis theorem for unitary matrices and of some results obtained by the author recently for diagonalizable pencils with real spectra.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
