Results 11 to 20 of about 849 (69)
α‐Derivations and their norm in projective tensor products of Γ‐Banach algebras
International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 2, Page 359-368, 1998., 1996 Let (V, Γ) and (V′, Γ′) be Gamma‐Banach algebras over the fields F1 and F2 isomorphic to a field F which possesses a real valued valuation, and (V, Γ)⊗p(V′, Γ′), their projective tensor product. It is shown that if D1 and D2 are α ‐ derivation and α′ ‐ derivation on (V, Γ) and (V′, Γ′) respectively and , is an arbitrary element of (V, Γ)⊗p(V′, Γ ...
T. K. Dutta, H. K. Nath, R. C. Kalita
wiley +1 more source
A note on the three-way generalization of the Jordan canonical form
Open Mathematics, 2018 The limit point 𝓧 of an approximating rank-R sequence of a tensor Ƶ can be obtained by fitting a decomposition (S, T, U) ⋅ 𝓖 to Ƶ. The decomposition of the limit point 𝓧 = (S, T, U) ⋅ 𝓖 with 𝓖 = blockdiag(𝓖1, … , 𝓖m) can be seen as a three order ...
Cui Lu-Bin, Li Ming-Hui
doaj +1 more source
A concise proof to the spectral and nuclear norm bounds through tensor partitions
Open Mathematics, 2019 On estimations of the lower and upper bounds for the spectral and nuclear norm of a tensor, Li established neat bounds for the two norms based on regular tensor partitions, and proposed a conjecture for the same bounds to be hold based on general tensor ...
Kong Xu
doaj +1 more source
Some inequalities on the spectral radius of nonnegative tensors
Open Mathematics, 2020 The eigenvalues and the spectral radius of nonnegative tensors have been extensively studied in recent years. In this paper, we investigate the analytic properties of nonnegative tensors and give some inequalities on the spectral radius.
Ma Chao +3 more
doaj +1 more source
Bound for the largest singular value of nonnegative rectangular tensors
Open Mathematics, 2016 In this paper, we give a new bound for the largest singular value of nonnegative rectangular tensors when m = n, which is tighter than the bound provided by Yang and Yang in “Singular values of nonnegative rectangular tensors”, Front. Math.
He Jun +4 more
doaj +1 more source
A note on the gap between rank and border rank [PDF]
, 2017 We study the tensor rank of the tensor corresponding to the algebra of n-variate complex polynomials modulo the dth power of each variable. As a result we find a sequence of tensors with a large gap between rank and border rank, and thus a counterexample
Zuiddam, Jeroen
core +3 more sources
Two new eigenvalue localization sets for tensors and theirs applications
Open Mathematics, 2017 A new eigenvalue localization set for tensors is given and proved to be tighter than those presented by Qi (J. Symbolic Comput., 2005, 40, 1302-1324) and Li et al. (Numer. Linear Algebra Appl., 2014, 21, 39-50).
Zhao Jianxing, Sang Caili
doaj +1 more source
Fast truncation of mode ranks for bilinear tensor operations [PDF]
, 2010 We propose a fast algorithm for mode rank truncation of the result of a bilinear operation on 3-tensors given in the Tucker or canonical form. If the arguments and the result have mode sizes n and mode ranks r, the computation costs $O(nr^3 + r^4)$.
Caroll +25 more
core +1 more source
On Comon's and Strassen's conjectures [PDF]
, 2018 Comon's conjecture on the equality of the rank and the symmetric rank of a symmetric tensor, and Strassen's conjecture on the additivity of the rank of tensors are two of the most challenging and guiding problems in the area of tensor decomposition.
Casarotti, Alex +2 more
core +2 more sources
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