Results 11 to 20 of about 835 (69)
Introduction to Grassmann manifolds and quantum computation
Journal of Applied Mathematics, Volume 2, Issue 8, Page 371-405, 2002., 2002 Geometrical aspects of quantum computing are reviewed elementarily for nonexperts and/or graduate students who are interested in both geometry and quantum computation. We show how to treat Grassmann manifolds which are very important examples of manifolds in mathematics and physics.
Kazuyuki Fujii
wiley +1 more source
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
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
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
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
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
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
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
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 +15 more
core +6 more sources
An S-type upper bound for the largest singular value of nonnegative rectangular tensors
Open Mathematics, 2016 An S-type upper bound for the largest singular value of a nonnegative rectangular tensor is given by breaking N = {1, 2, … n} into disjoint subsets S and its complement. It is shown that the new upper bound is smaller than that provided by Yang and Yang (
Zhao Jianxing, Sang Caili
doaj +1 more source