Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Symmetric completions and products of symmetric matrices
HTML articles powered by AMS MathViewer

by Morris Newman PDF
Trans. Amer. Math. Soc. 186 (1973), 191-201 Request permission

Abstract:

We show that any vector of n relatively prime coordinates from a principal ideal ring R may be completed to a symmetric matrix of ${\text {SL}}(n,R)$, provided that $n \geq 4$. The result is also true for $n = 3$ if R is the ring of integers Z. This implies for example that if F is a field, any matrix of ${\text {SL}}(n,F)$ is the product of a fixed number of symmetric matrices of ${\text {SL}}(n,F)$ except when $n = 2$, $F = {\text {GF}}(3)$, which is a genuine exception.
References
    C. C. MacDuffee, The theory of matrices, Chelsea, New York, 1946.
  • Morris Newman, Integral matrices, Pure and Applied Mathematics, Vol. 45, Academic Press, New York-London, 1972. MR 0340283
  • Olga Taussky, The role of symmetric matrices in the study of general matrices, Linear Algebra Appl. 5 (1972), 147–154. MR 302674, DOI 10.1016/0024-3795(72)90024-9
  • Olga Taussky, The factorization of an integral matrix into a product of two integral symmetric matrices. I, Acta Arith. 24 (1973), 151–156. MR 335551, DOI 10.4064/aa-24-2-151-156
  • —, The factorization of an integral matrix into a product of two integral symmetric matrices. II, Comm. Pure Appl. Math. (to appear).
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 15A33
  • Retrieve articles in all journals with MSC: 15A33
Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 186 (1973), 191-201
  • MSC: Primary 15A33
  • DOI: https://doi.org/10.1090/S0002-9947-1973-0485931-7
  • MathSciNet review: 0485931