Related papers: Interactions Between the Generalized Hadamard Prod…
We construct the tensor product for f-algebras, including proving a universal property for it, and investigate how it preserves algebraic properties of the factors.
Developed in a series of seminal papers in the early 2010s, the tubal tensor framework provides a clean and effective algebraic setting for tensor computations, supporting matrix-mimetic features such as a tensor Singular Value…
Hankel tensors arise from applications such as signal processing. In this paper, we make an initial study on Hankel tensors. For each Hankel tensor, we associate it with a Hankel matrix and a higher order two-dimensional symmetric tensor,…
We focus upon the relationship between Hamiltonian cycle products and efficient vectors for a reciprocal matrix $A$, to more deeply understand the latter. This facilitates a new description of the set of efficient vectors (as a union of…
We generalize the embedding formalism for conformal field theories to the case of general operators with mixed symmetry. The index-free notation encoding symmetric tensors as polynomials in an auxiliary polarization vector is extended to…
It is demonstrated how an explicit expression of the (partial) sum of Tetranacci numbers can be found and proved using generating functions and the Hadamard product. We also provide a Binet-type formula for generalized Fibonacci numbers, by…
We present a method to construct new tilting complexes from existing ones using tensor products, generalizing a result of Rickard. The endomorphism rings of these complexes are generalized matrix rings that are "componentwise" tensor…
We show that any scalar differential operator with a family of polyno- mials as its common eigenfunctions leads canonically to a matrix differen- tial operator with the same property. The construction of the correspond- ing family of matrix…
Let C be a coalgebra over a field k and A its dual algebra. The category of C-comodules is equivalent to a category of A-modules. We use this to interpret the cotensor product M \square N of two comodules in terms of the appropriate…
This survey provides an elementary introduction to operads and to their applications in homotopical algebra. The aim is to explain how the notion of an operad was prompted by the necessity to have an algebraic object which encodes higher…
The main aim of the present note is to prove new Hadamard like integral inequalities for the product of the convex functions.
We consider certain matrix-products where successive matrices in the product belong alternately to a particular qualitative class or its transpose. The main theorems relate structural and spectral properties of these matrix-products to the…
We describe a formula for computing the product of the Young symmetrizer of a Young tableau with the Young symmetrizer of a subtableau, generalizing the classical quasi-idempotence of Young symmetrizers. We derive some consequences to the…
The $\star_M$-family of tensor-tensor products is a framework which generalizes many properties from linear algebra to third order tensors. Here, we investigate positive semidefiniteness and semidefinite programming under the…
In this paper, some tensor commutation matrices are expressed in termes of the generalized Pauli matrices by tensor products of the Pauli matrices.
The simple product formulae for derivatives of scalar functions raised to different powers are generalized for functions which take values in the set of symmetric positive definite matrices. These formulae are fundamental in derivation of…
The product of smooth valuations on manifolds is described in terms of differential forms, Gelfand transforms and blow-up spaces. It is shown that the product extends partially to generalized valuations and corresponds geometrically to…
Inspired from modern out-of-equilibrium statistical physics models, a matrix product based framework permits the formal definition of random vectors (and random time series) whose desired joint distributions are a priori prescribed. Its key…
We define generalised higher Whitehead maps between polyhedral products. By investigating the interplay between the homotopy-theoretic properties of polyhedral products and the combinatorial properties of simplicial complexes, we describe…
We use a smoothed version of the explicit formula to find an approximation to the Riemann zeta function as a product over its nontrivial zeros multiplied by a product over the primes. We model the first product by characteristic polynomials…