Integral matrices as diagonal quadratic forms. Issue 4 (3rd April 2018)

• Record Type: Journal Article
• Authors: Lee, Jungin
• Is Part Of: Linear & multilinear algebra. Volume 66:Issue 4(2018)
• Page Start: 742
• Page End: 747
• Publication Date: 2018-04-03
• Subjects: Integral matrix -- diagonal quadratic form -- sum of matrices; 15A24 -- 15B36; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2017.1320965
• Languages: English
• ISSNs: 0308-1087

Abstract

ABSTRACT: In this paper, we investigate the conditions under which a diagonal quadratic form ∑ i = 1 m a i X i 2 represents every n × n integral matrix, where a i ( 1 ≤ i ≤ m ) are integers. For n = 2, we give a necessary and sufficient condition. Also we give some sufficient conditions for each n ≥ 2 where a i ( 1 ≤ i ≤ m ) are pairwise coprime.