Let A = (a j ) be an orthogonal matrix with no entries zero. Let B = (b j ) be the matrix defined by b j = 1 ai j . M. Kontsevich conjectured that the rank of B is never equal to three. We interpret this conjecture geometrically and prove it. The geometric statment can be understood as a generalization of the Castelnouvo lemma and Brianchon’s theorem in algebraic geometry. §1. Definitions and S...

We introduce power Hadamard matrices, in order to study the structure of (group) generalized Hadamard matrices, Butson (generalized) Hadamard matrices and other related orthogonal matrices, with which they share certain common characteristics. The new objects turn out to be as interesting, and perhaps as useful, as the objects that motivated them. We develop a basic theory of power Hadamard mat...

In this paper we obtain some Hadamard type inequalities for triple integrals. The results generalize those obtained in (S.S. DRAGOMIR, On Hadamard’s inequality for the convex mappings defined on a ball in the space and applications, RGMIA (preprint), 1999).

This paper addresses aspects of channel coding in orthogonal frequency-division multiplexing–code-division multiple access (OFDM-CDMA) uplink systems where each user occupies a bandwidth much larger than the information bit rate. This inherent bandwidth expansion allows the application of powerful low-rate codes under the constraint of low decoding costs. Three different coding strategies are c...

Spacetime, understood as a globally hyperbolic manifold, may be characterized by spectral data using a 3+1 splitting into space and time, a description of space by spectral triples and by employing causal relationships, as proposed earlier. Here, it is proposed to use the Hadamard condition of quantum field theory as a smoothness principle.

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...

We study the Steiner problem of finding a minimal spanning network in the setting of a space of probability measures with metric defined by cost of optimal transport between measures. Existence of a solution is shown for the Wasserstein space Pp(X ) over any base space X which is a separable, locally compact Hadamard space. Structural results are given for the case p = 2 under further restricti...

Shi and Aharonov have shown that the Toffoli gate and the Hadamard gate give rise to an approximately universal set of quantum computational gates. The basic algebraic properties of this system have been studied in Dalla Chiara et al. (Foundations of Physics 39(6):559–572, 2009), where we have introduced the notion of Shi-Aharonov quantum computational structure. In this paper we propose an alg...

We propose a fast algorithm for ridge regression when the number of features is much larger than the number of observations (p n). The standard way to solve ridge regression in this setting works in the dual space and gives a running time of O(np). Our algorithm Subsampled Randomized Hadamard TransformDual Ridge Regression (SRHT-DRR) runs in time O(np log(n)) and works by preconditioning the de...

Recently, a general class of the Hermit--Hadamard-Fejer inequality on convex functions is studied in [H. Budak, March 2019, 74:29, textit{Results in Mathematics}]. In this paper, we establish a generalization of Hermit--Hadamard--Fejer inequality for fractional integral based on co-ordinated convex functions.Our results generalize and improve several inequalities obtained in earlier studies.