Sums of squares of matrices

Morris Newman

Vol. 118 (1985), No. 2, 497–506

DOI: 10.2140/pjm.1985.118.497

Abstract

The principal results of this paper are the following: Every integral 2 × 2 matrix is the sum of at most 3 integral squares, and this is best possible. Every integral n×n matrix with n > 2 is the sum of at most k integral squares, where k = 7 if n is even, and k = 9 if n is odd. Every n × n matrix over GF(2) is the sum of at most 2 matrix squares, and this is best possible.

Mathematical Subject Classification 2000

Primary: 15A36

Secondary: 05B20, 11C20, 15A33

Milestones

Received: 13 February 1984

Published: 1 June 1985