Results 21 to 30 of about 849 (68)

Decomposition of homogeneous polynomials with low rank [PDF]

, 2010
Let $F$ be a homogeneous polynomial of degree $d$ in $m+1$ variables defined over an algebraically closed field of characteristic zero and suppose that $F$ belongs to the $s$-th secant varieties of the standard Veronese variety $X_{m,d}\subset \mathbb{P}^
A. Bernardi, Alessandra Bernardi, C. Ciliberto, C. Ciliberto, Edoardo Ballico, G. Comas, J. Alexander, J. Brachat, J.M. Landsberg, K. Ranestad, L. Chiantini, L.-H. Lim, M. Mella, M. Mella, M.C. Brambilla, P. Comon   +15 more
core   +6 more sources

New bounds for the minimum eigenvalue of 𝓜-tensors

Open Mathematics, 2017
A new lower bound and a new upper bound for the minimum eigenvalue of an 𝓜-tensor are obtained. It is proved that the new lower and upper bounds improve the corresponding bounds provided by He and Huang (J. Inequal.
Zhao Jianxing, Sang Caili
doaj   +1 more source

Note on a Differential-Geometrical Construction of Optimal Directions in Linearly-Constrained Systems [PDF]

, 2010
This note presents an analytic construction of the optimal unit-norm direction hat(x) = x/|x| that maximizes or minimizes the objective linear expression, B . hat(x), subject to a system of linear constraints of the form [A] .
Ellis, John, Lee, Jae Sik, Pilaftsis, Apostolos   +2 more
core  

Characterization generalized derivations of tensor products of nonassociative algebras

Demonstratio Mathematica
Consider A{\mathcal{A}} and ℬ{\mathcal{ {\mathcal B} }} to be nonassociative unital algebras. Under the assumption that either one of them has finite dimensions or that both are finite dimensions, a generalized derivation is an additive map ℱ:A→A ...
Aboubakr Ahmed
doaj   +1 more source

On the average condition number of tensor rank decompositions

, 2019
We compute the expected value of powers of the geometric condition number of random tensor rank decompositions. It is shown in particular that the expected value of the condition number of $n_1\times n_2 \times 2$ tensors with a random rank-$r ...
Breiding, Paul, Vannieuwenhoven, Nick
core   +1 more source

Matrix stretching

Open Mathematics
We consider the tensor products of square matrices of different sizes and introduce the stretching maps, which can be viewed as a generalized matricization.
Futorny Vyacheslav, Neklyudov Mikhail, Zhao Kaiming   +2 more
doaj   +1 more source

Hyperdeterminants on semilattices [PDF]

, 2006
We compute hyperdeterminants of hypermatrices whose indices belongs in a meet-semilattice and whose entries depend only of the greatest lower bound of the indices. One shows that an elementary expansion of such a polynomial allows to generalize a theorem
Luque, Jean-Gabriel
core   +4 more sources

Maximizing spectral radii of uniform hypergraphs with few edges

, 2015
In this paper we investigate the hypergraphs whose spectral radii attain the maximum among all uniform hypergraphs with given number of edges. In particular we characterize the hypergraph(s) with maximum spectral radius over all unicyclic hypergraphs ...
Fan, Yi-Zheng, Liu, An-Hong, Peng, Xi-Xi, Tan, Ying-Ying   +3 more
core   +1 more source

Three Dimensional Strongly Symmetric Circulant Tensors

, 2015
In this paper, we give a necessary and sufficient condition for an even order three dimensional strongly symmetric circulant tensor to be positive semi-definite.
Chen, Yannan, Qi, Liqun, Wang, Qun
core   +1 more source

A conjecture on the primitive degree of Tensors [PDF]

, 2013
In this paper, we prove: Let A be a nonnegative primitive tensor with order m and dimension n. Then its primitive degree R(A)\leq (n-1)^2+1, and the upper bound is sharp.
He, Zilong, You, Lihua, Yuany, Pingzhi
core