Norms on Direct Sums and Tensor Products

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1972Publisher:JSTORJournal:Mathematics of Computation, volume 26, page 401 (issn: 0025-5718,

Copyright policy )

Authors: Lancaster, P.; Farahat, H. K.;

doi: 10.2307/2005167 , 10.1090/s0025-5718-1972-0305099-x

Norms on Direct Sums and Tensor Products

- Summary
- Subjects
- Metrics

Abstract

We first consider the construction of a norm on a direct sum of normed linear spaces and call a norm absolute if it depends only on the norms of the component spaces. Several characterizations are given of absolute norms. Absolute norms are then used to construct norms on tensor products of normed linear spaces and on tensor products of operators on normed linear spaces.

Keywords

Numerical computation of matrix norms, conditioning, scaling, Multilinear algebra, tensor calculus, Norms of matrices, numerical range, applications of functional analysis to matrix theory

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	9
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Top 10%
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average