Given matrices of the same size, A = a ij ] and B = b ij ], we deene their Hadamard Product to be A B = a ij b ij ]. We show that if x i > 0 and q p 0 then the n n matrices q j # are positive deenite and relate these facts to some matrix valued arithmetic-geometric-harmonic mean inequalities-some of which involve Hadamard products and others unitarily invariant norms. It is known that if A is p...

F2F is a C++ library for large-scale machine learning. It contains a CPU optimized implementation of the Fastfood algorithm in Le et al. (2013), that allows the computation of approximated kernel expansions in loglinear time. The algorithm requires to compute the product of Walsh-Hadamard Transform (WHT) matrices. A cache friendly SIMD Fast Walsh-Hadamard Transform (FWHT) that achieves compelli...

In this article, experimental situations are considered where a main effects plan is to be used to study m two-level factors using n runs which are partitioned into b blocks, not necessarily of same size. Assuming the block sizes to be even for all blocks, for the case n ≡ 2 (mod 4), optimal designs are obtained with respect to type 1 and type 2 optimality criteria in the class of designs provi...

The concept of semi-regular sets of matrices was introduced by J. Seberry in "A new construction for Williamson-type matrices", Graphs and Combinatorics, 2(1986), 81-87. A regular s-set of matrices of order m was first discovered by J. Seberry and A. L. Whiteman in "New Hadamard matrices and conference matrices obtained via Mathon's construction", Graphs and Combinatorics, 4(1988), 355-377. In ...

The Fourier Transform Sum-Product Algorithm (FT-SPA) used in non-binary Low-Density Parity-Check (LDPC) decoding makes extensive use of the Walsh-Hadamard Transform (WHT). We have developed a massively parallel Fast Walsh-Hadamard Transform (FWHT) which exploits the Graphics Processing Unit (GPU) pipeline and memory hierarchy, thereby minimizing the level of memory bank conflicts and maximizing...

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...

Some prosperities of matrix product are presented in the paper, Kronecker product, Khatri-Rao product, Hadamard product and outer product are involved. And we get some results that a multilinear tensor can be represented by the product of matrix product for a three order tensor. For higher tensor, we conjure that the same results also hold. By the representation of matrix, we give an iterative ...

The library explores the applicability of Hadamard as an input modulator for problems classification. It introduces a framework in C++ to use kernel approximates mini-batch setting with Stochastic Gradient Descent. algorithm requires compute product matrices Walsh Hadamard. A free-standing cache friendly Fast that achieves compelling speed is provided, well lightweight efficient CPU implementat...

In this paper, we introduce a new class of functions which are analytic and univalent with negative coefficients defined by using certain fractional operators described in the Caputo sense. Characterization property, the results on modified Hadamard product and integral transforms are discussed. Further, distortion theorem and radii of starlikeness and convexity are also determined here. Resume...