Multigraded Sylvester forms, duality and elimination matrices

Complex Hadamard Matrices from Sylvester Inverse Orthogonal Matrices

A novel method to obtain parameterizations of complex inverse orthogonal matrices is provided. These matrices are natural generalizations of complex Hadamard matrices which depend on non zero complex parameters. The method we use is via doubling the size of inverse complex conference matrices. When the free parameters take values on the unit circle the inverse orthogonal matrices transform into...

On Permanents of Sylvester Hadamard Matrices

It is well-known that a Sylvester Hadamard matrix can be described by means of a cocycle. In this paper it is shown that the additional internal structure in a Sylvester Hadamard matrix, provided by the cocycle, is su cient to guarantee some kind of reduction in the computational complexity of calculating its permanent using Ryser's formula. A Hadamard matrix H of order n is an n× n matrix with...

A Generalized Sylvester Identity and Fraction-free Random Gaussian Elimination

Sylvester's identity is a well-known identity which can be used to prove that certain Gaussian elimination algorithms are fraction-free. In this paper we will generalize Sylvester's identity and use it to prove that certain random Gaussian elimination algorithms are fraction-free. This can be used to yield fraction-free algorithms for solving Ax = b (x 0) and for the simplex method in linear pr...

String Duality and Modular Forms

Tests of duality between heterotic strings onK3×T 2 (restricted on certain Narain moduli subspaces) and type IIA strings on K3-fibered Calabi-Yau threefolds are attempted in the weak coupling regime on the heterotic side by identifying pertinent modular forms related to the computations of string threshold corrections. Concretely we discuss in parallel the three cases associated with Calabi-Yau...

Matrices in Elimination Theory