Vol. 23, No. 3, 1967

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ISSN: 0030-8730
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