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hyperdeterminant

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Hyperdeterminant - Wikipedia
A hyperdeterminant is defined on a multidimensional array of numbers or tensor. Like a determinant, the hyperdeterminant is a homogeneous polynomial with ... en.wikipedia.org
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Hyperdeterminant -- from Wolfram MathWorld
A technically defined extension of the ordinary determinant to higher dimensional hypermatrices. Cayley (1845) originally coined the term. mathworld.wolfram.com
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[1301.0472] Introduction to the hyperdeterminant and to the rank of ...
This is an introduction to the hyperderminant, according to Gelfand, Kapranov and Zelevinsky. The triangle inequality, characterizing the Segre varieties. arxiv.org
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hyperdeterminant
hyperdeˈterminant, n. and a. Math. [See hyper- 3.] a. n. A determinant of operative symbols; a symbolic expression for an invariant or covariant: invented by Cayley. b. adj. Of the nature of a hyperdeterminant.1845 Cayley in Camb. Math. Jrnl. IV. 195 The function u whose properties we proceed to inv... Oxford English Dictionary
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hyperdeterminant in nLab
The concept of Hyperdeterminant (or Cayley determinant) is a generalization of the concent of determinant to multidimensional matrices. ncatlab.org
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(PDF) Introduction to the Hyperdeterminant and to the Rank of ...
... In such cases, the defining equation of X ∨ n1,n2,n3 is the so-called hyperdeterminant, denoted by H n1,n2,n3 . See [GKZ08, Ott13] . 2.2. ... www.researchgate.net
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hyperdeterminant of a multidimensional matrix - Macaulay2
determinant(MultidimensionalMatrix) -- hyperdeterminant of a multidimensional matrix. The source of this document is in SparseResultants.m2:1474:0. macaulay2.com
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Tensor slice rank and Cayley's first hyperdeterminant - ScienceDirect
Cayley's first hyperdeterminant is a straightforward generalization of determinants for tensors. We prove that nonzero hyperdeterminants imply lower bounds on ... www.sciencedirect.com
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[PDF] Hyperdeterminant and Tensor Rank
This may also be taken as an alternative definition of the hyperdeterminant. ∆(A). ... Hyperdeterminant of A = [[a ijk. ]] ∈ R. 2×2×3 is. ∆(A) = det. www.stat.uchicago.edu
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Cayley's First Hyperdeterminant is an Entanglement Measure - arXiv
In this paper, we rigorously prove that Cayley's first hyperdeterminant is an entanglement measure on 2n-qudits, and thus a legitimate generalization of the ... arxiv.org
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Cayley's hyperdeterminant, the principal minors of a symmetric ...
It has recently been shown that there is a connection between Cayley's hypdeterminant and the principal minors of a symmetric matrix. ieeexplore.ieee.org
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Multipartite entanglement
In particular concurrence and tangle are special cases of hyperdeterminant. Indeed for two qubits concurrence is simply the modulus of the determinant, which is the hyperdeterminant of first order; whereas the tangle is the hyperdeterminant wikipedia.org
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hyper-
hyper-, prefix (haɪpə(r)) repr. Gr. ὑπερ- (ὑπέρ prep. and adv., ‘over, beyond, over much, above measure’); in Gr. combined adverbially with verbs, in the local sense ‘over, above, beyond’, as ὑπερβαίνειν to step over, overstep, cross, ὑπερβάλλειν to throw over or beyond; and hence in the adjectives ... Oxford English Dictionary
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List of things named after Arthur Cayley
algebra Cayley–Klein metric Cayley–Klein model of hyperbolic geometry Cayley–Menger determinant Cayley–Purser algorithm Cayley's formula Cayley's hyperdeterminant wikipedia.org
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Arthur Cayley
consequently the Cayley Formation, a geological unit named after the crater) Cayley's mousetrap — a card game Cayleyan Chasles–Cayley–Brill formula Hyperdeterminant wikipedia.org
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