Products of positive definite matrices. I

Charles Ballantine

Vol. 23 (1967), No. 3, 427–433

DOI: 10.2140/pjm.1967.23.427

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,⋯,P_n, it is shown that P₁,P₂,⋯,P_n, and S must satisfy a condition which roughly speaking measures by how much (depending on S) P_I,P_z,⋯,P_n must collectively differ from scalar matrices.

Mathematical Subject Classification

Primary: 15.60

Milestones

Received: 11 August 1966

Published: 1 December 1967