On Some Determinantal Inequalities

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Apr 1968Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 19, page 462 (issn: 0002-9939,

Copyright policy )

Authors: Carlson, David;

doi: 10.2307/2035552 , 10.1090/s0002-9939-1968-0225801-6

On Some Determinantal Inequalities

- Summary
- Subjects
- Metrics

Abstract

1. We shall discuss two recent theorems by Marvin Marcus ([6, Theorem 3]) and Ky Fan ( [4, Theorem 1 ]) involving related determinantal inequalities. We give improvements of their inequalities, and show how they follow from the previously known special cases of the theorems. We deal with real or complex matrices A of order n. For any subset 3 of { 1, * , n }, we denote by A (3) the principal minor on the rows and columns of A indexed by 3; clearly the order in -which the indices of : occur is irrelevant. We define A (0) = 1. Now let 31, * * *, 13k be subsets of { 1, , n }, and h a positive integer between 1 and k; we define

Keywords

linear algebra, forms

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).	3
	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.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Top 10%
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average