29 May
2007
29 May
'07
12:20 p.m.
Fred writes: << A matrix A of order n is "cyclic" when A[i,j] is a function only of (i-j)(mod n), and "0-1" when A[i,j] € {0,1}. What is a criterion for such a matrix to be singular (over the integers)? What is the maximum absolute value of its determinant as a function of n?
The paper (Determinants of binary circulant matrices. Proceedings of the ISIT, 2004) appears to discuss this question, but it requires a subscription or download fee. < http://ieeexplore.ieee.org/Xplore/login.jsp?url=/iel5/9423/29909/01365161.pd... >. Many references to this question mention "Hadamard bounds" or "Gram-Hadamard bounds" -- whatever that means -- on the size of a determinant. --Dan