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Hyperdeterminant

In algebra, the hyperdeterminant is a generalization of the determinant. Whereas a determinant is a scalar valued function defined on an n × n square matrix, a hyperdeterminant is defined on a multidimensional array of numbers or tensor. Like a determinant, the hyperdeterminant is a homogeneous polynomial with integer coefficients in the components of…

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Overview

Cayley's second hyperdeterminant Det

Other general hyperdeterminants related to Cayley's Det

Properties of hyperdeterminants

History and applications

Sources

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Hyperdeterminant

Nodes64
Edges63
Triples143
Avg. degree1.97
Density0.03125
Components1

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Hyperdeterminant

Top relations

related to Sources · 71
Hyperdeterminant → Advances, Alon, Applied Mathematics, April, Arthur Cayley, Australian Mathematical Society, Baltimore, Bibcode, Birkhäuser, Boston, Bulletin, Camb, Cambridge Math, Carla, Cayley, Cayley's, Classification, Crilly, David, Determinant Tensor
related to Further reading · 23
Hyperdeterminant → Ad, Determinanti, Determinants, Die Determinanten, Dimensions, For, Gand, Gel'fand, German, Halle, Histoire, Hoepli, Hoste, Kapranov, Lecat, Leitzmann, Leçons, Maurice, Milan, Pascal
related to history · 12
Hyperdeterminant → Alon-Tarsi, Arthur Cayley, Cayley, Cayley's, For, Gel'fand, Indeed, Kapranov, Since, The, This, Zelevinsky
related to Cayley's second hyperdeterminant Det · 6
Hyperdeterminant → Arthur Cayley, British, Cayley's, In, The, This
related to Examples · 6
Hyperdeterminant → Applying, Each, In, SX, The, YS
related to Multiplicative properties · 6
Hyperdeterminant → Binet-Cauchy, For, However, One, The, This
related to Invariance properties · 5
Hyperdeterminant → In, SL, The, This, Using
is a · 4
Hyperdeterminant → algebraic invariant under the action of the special linear group SL, discriminant of a polynomial, generalization of the determinant, homogeneous polynomial with integer coefficients in the components of the tensor
related to Degree · 4
Hyperdeterminant → For, In, Nr, Since
related to As a discriminant · 2
Hyperdeterminant → For, Then Det

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Important terminology

hyperdeterminants cayley's second determinant format hypermatrix determinants discriminant first case det degree cayley tensor algebraic polynomial one dimensions defined general

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Hyperdeterminantis ageneralization of the determinant0.90text
Hyperdeterminantis ahomogeneous polynomial with integer coefficients in the components of the tensor0.90text
Hyperdeterminantis adiscriminant of a polynomial0.90text
Hyperdeterminantis aalgebraic invariant under the action of the special linear group SL0.90text
Hyperdeterminantrelated to As a discriminantFor0.60section
Hyperdeterminantrelated to As a discriminantThen Det0.60section
Hyperdeterminantrelated to Cayley's second hyperdeterminant DetIn0.60section
Hyperdeterminantrelated to Cayley's second hyperdeterminant DetCayley's0.60section
Hyperdeterminantrelated to Cayley's second hyperdeterminant DetBritish0.60section
Hyperdeterminantrelated to Cayley's second hyperdeterminant DetArthur Cayley0.60section
Hyperdeterminantrelated to Cayley's second hyperdeterminant DetThe0.60section
Hyperdeterminantrelated to Cayley's second hyperdeterminant DetThis0.60section

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