Vol. 15, No. 3, 1965

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Vol. 286: 1  2
Vol. 285: 1  2
Vol. 284: 1  2
Vol. 283: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Subscriptions
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
A subdeterminant inequality

Marvin David Marcus and H. Minc

Vol. 15 (1965), No. 3, 921–924
Abstract

Let A be an n-square positive semi-definite hermitian matrix and let Dm(A) denote the maximum of all order m principal subdeterminants of A. In this note we prove the inequality

(Dm (A ))1∕m ≧ (Dm+1 (A ))1∕(m+1),  m = 1,⋅⋅⋅ ,n− 1,

and discuss in detail the case of equality. This result is closely related to Newton’s and Szász’s inequalities.

Mathematical Subject Classification
Primary: 15.58
Secondary: 15.20
Milestones
Received: 27 August 1964
Published: 1 September 1965
Authors
Marvin David Marcus
H. Minc