IJPAM: Volume 34, No. 2 (2007)

DETERMINANT EVALUATIONS FOR
WEIGHING MATRICES

Christos Kravvaritis$^1$, Marilena Mitrouli$^2$
$^{1,2}$Department of Mathematics
University of Athens
Panepistimiopolis, Athens, 15784, GREECE
$^1$email: [email protected]
$^2$email: [email protected]


Abstract.In the present paper we are interested in calculating the minors of weighing matrices $W(n,n-k)$ for $k\geq 1$. By using appropriate determinant manipulations we obtain formulas for the minors of order $n-1,~n-2$ and $n-3$ of a $W(n,n-1)$ and show how these ideas can be similarly applied to determinant evaluations for $W(n,n-k)$ generally. We demonstrate the proof of the most generalized version of the Determinant Simplification Theorem and show how it can be used for the evaluation of minors of order $n-j$, $j\geq 1$, of weighing matrices. Application to numerical analysis connected with the growth problem is also given.

Received: October 6, 2006

AMS Subject Classification: 15A15, 05B20, 65F40, 65F05, 65G50

Key Words and Phrases: determinants, weighing matrices, symbolic computation, Gaussian elimination, complete pivoting, growth problem

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 34
Issue: 2