Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-23T19:08:04.254Z Has data issue: false hasContentIssue false
  • English
  • Français

Scalar matrix quadratic residues

Published online by Cambridge University Press:  26 February 2010

Gordon Pall  and
Olga Taussky
Gordon Pall
Affiliation:
Louisiana State University, California Institute of Technology.
Olga Taussky
Affiliation:
Louisiana State University, California Institute of Technology.
Get access

Extract

No systematic study seems to have been made of so natural a question as the analogue for matrices of quadratic residues. One generalization of x2 (x an integer) is X2 (X an integral matrix). Another is X′ X, where the prime means “transpose”. We study here the solvability for X of the congruence

where p is a prime, r ≥ 1; I (the identity matrix) and X are n-by-n; and a is an integer not divisible by p2.

Type
Research Article
Information
Mathematika , Volume 12 , Issue 1 , June 1965 , pp. 94 - 96
Copyright
Copyright © University College London 1965

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Lagrange, J. L., Mém. Acad. Berlin, 1770.Google Scholar
2. Hilbert, D., Ges. Abhandlungen I (Springer, 1932, p. 164).CrossRefGoogle Scholar
3. Jones, B. W., The arithmetic theory of quadratic forms (Carus Mathematical Monograph, 1950).CrossRefGoogle Scholar
4. Pall, G., “The arithmetical invariants of quadratic forms”, Bull. American Math. Soc, 51 (1945), 185–197.CrossRefGoogle Scholar