Vol. 23, No. 3, 1967

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 325: 1
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Vol. 320: 1  2
Vol. 319: 1  2
Vol. 318: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
Products of positive definite matrices. I

Charles Ballantine

Vol. 23 (1967), No. 3, 427–433
Abstract

For each positive integer n, this paper gives necessary and sufficient conditions (nasc) on a 2 × 2 real matrix S (of positive determinant) that S be a product of n positive definite real (symmetric 2 × 2) matrices. Also, when S is the product of (real 2 × 2) positive definite matrices P1,P2,,Pn, it is shown that P1,P2,,Pn, and S must satisfy a condition which roughly speaking measures by how much (depending on S) PI,Pz,,Pn must collectively differ from scalar matrices.

Mathematical Subject Classification
Primary: 15.60
Milestones
Received: 11 August 1966
Published: 1 December 1967
Authors
Charles Ballantine