We prove that if there exist Hadamard matrices of order 4m, 4n, 4p, and 4q then there exists an Hadamard matrix of order 16mnpq. This improves and extends the known result of Agayan that there exists a Hadamard matrix of order 8mn if there exist Hadamard matrices of order 4m and 4n. Disciplines Physical Sciences and Mathematics Publication Details R. Craigen, Jennifer Seberry and Xian-Mo Zhang,...

In this work we propose a generalization of the Hadamard product between two matrices to a tensor-valued, multi-linear product between k matrices for any k ≥ 1. A multi-linear dual operator to the generalized Hadamard product is presented. It is a natural generalization of the Diag x operator, that maps a vector x ∈ R into the diagonal matrix with x on its main diagonal. Defining an action of t...

In this article we explain the link between Pohlen’s extended Hadamard product and holomorphic cohomological convolution on $\mathbb{C}^\*$. For purpose introduce a generalized product, which is defined even if functions do not vanish at infinity, as well notion of strongly convolvable sets.

In this paper we introduce the concept of geometrically quasiconvex functions on the co-ordinates and establish some Hermite-Hadamard type integral inequalities for functions defined on rectangles in the plane. Some  inequalities for product of two geometrically quasiconvex functions on the co-ordinates are considered.

Let A and B be nonnegative matrices. A new upper bound on the spectral radius ρ(A◦B) is obtained. Meanwhile, a new lower bound on the smallest eigenvalue q(A B) for the Fan product, and a new lower bound on the minimum eigenvalue q(B ◦A−1) for the Hadamard product of B and A−1 of two nonsingular M -matrices A and B are given. Some results of comparison are also given in theory. To illustrate ou...

We present a comparative study of four product operators on weighted languages: (i) the convolution, (ii) the shuffle, (iii) the infiltration, and (iv) the Hadamard product. Exploiting the fact that the set of weighted languages is a final coalgebra, we use coinduction to prove that a classical operator from difference calculus in mathematics: the Newton transform, generalises (from infinite se...