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# On norms of principal submatrices

Publikationstyp

Journal Article

Publikationsdatum

2021-07

Sprache

English

Institut

TORE-URI

Enthalten in

Volume

620

Start Page

27

End Page

36

Citation

Linear Algebra and Its Applications 620: 27-36 (2021-07)

Publisher DOI

Scopus ID

Let a norm on the set Mn of real or complex n-by-n matrices be given. We investigate the question of finding the largest constants αn and βn such that for each A∈Mn the average of the norms of its (n−1)-by-(n−1) principal submatrices is at least αn times the norm of A, and such that the maximum of the norms of those principal submatrices is at least βn times the norm of A. For a variety of classical norms including induced ℓp-norms, weakly unitarily invariant norms, and entrywise norms we give lower and upper bounds for αn and βn. In several cases αn and βn are explicitly determined.