Symmetric completions and products of symmetric matrices
Author:
Morris Newman
Journal:
Trans. Amer. Math. Soc. 186 (1973), 191201
MSC:
Primary 15A33
MathSciNet review:
0485931
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
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 , provided that . The result is also true for if R is the ring of integers Z. This implies for example that if F is a field, any matrix of is the product of a fixed number of symmetric matrices of except when , , which is a genuine exception.
 [1]
C. C. MacDuffee, The theory of matrices, Chelsea, New York, 1946.
 [2]
Morris
Newman, Integral matrices, Academic Press, New YorkLondon,
1972. Pure and Applied Mathematics, Vol. 45. MR 0340283
(49 #5038)
 [3]
Olga
Taussky, The role of symmetric matrices in the study of general
matrices, Linear Algebra and Appl. 5 (1972),
147–154. MR 0302674
(46 #1818)
 [4]
Olga
Taussky, The factorization of an integral matrix into a product of
two integral symmetric matrices. I, Acta Arith. 24
(1973), 151–156. Collection of articles dedicated to Carl Ludwig
Siegel on the occasion of his seventyfifth birthday, II. MR 0335551
(49 #332)
 [5]
, The factorization of an integral matrix into a product of two integral symmetric matrices. II, Comm. Pure Appl. Math. (to appear).
 [1]
 C. C. MacDuffee, The theory of matrices, Chelsea, New York, 1946.
 [2]
 M. Newman, Integral matrices, Academic Press, New York, 1972. MR 0340283 (49:5038)
 [3]
 O. Taussky, The role of symmetric matrices in the study of general matrices, Linear Algebra and Appl. 5 (1972), 147154. MR 0302674 (46:1818)
 [4]
 , The factorization of an integral matrix into a product of two integral symmetric matrices. I, Acta Arith. (to appear). MR 0335551 (49:332)
 [5]
 , 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
DOI:
http://dx.doi.org/10.1090/S00029947197304859317
PII:
S 00029947(1973)04859317
Keywords:
Principal ideal rings,
fields,
symmetric matrices,
unimodular matrices,
symmetric completion
Article copyright:
© Copyright 1973
American Mathematical Society
