Hyperdeterminant From Wolfram Mathworld

Integration From Wolfram Mathworld Weisstein, eric w. "hyperdeterminant." from mathworld a wolfram resource. mathworld.wolfram hyperdeterminant . a technically defined extension of the ordinary determinant to "higher dimensional" hypermatrices. Wolfram language function: compute the hyperdeterminant for a given hypermatrix (a multidimensional array of complex numbers). complete documentation and usage examples. download an example notebook or open in the cloud.

Supremum From Wolfram Mathworld Compute answers using wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. for math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music…. 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. Proposition 5.2. (i) for matrices a of format 2 b b and 3 b b the discriminant of det ~a(x) coincides with the hyperdeterminant of a. (ii) for matrices a of format 4 b b the discriminant of det ~a(x) is equal to the product of the hyperdeterminant and an extra factor which is a square. The explicit computation of the hyperdeterminant presented from the very beginning exceptional difficulties.

Hyperdeterminant From Wolfram Mathworld Proposition 5.2. (i) for matrices a of format 2 b b and 3 b b the discriminant of det ~a(x) coincides with the hyperdeterminant of a. (ii) for matrices a of format 4 b b the discriminant of det ~a(x) is equal to the product of the hyperdeterminant and an extra factor which is a square. The explicit computation of the hyperdeterminant presented from the very beginning exceptional difficulties. This fact leads us to expect that the hyperdeterminant will cancel out in more pieces than the ones that has already been shown. we will see in theorem 3.8 that these new pieces will live inside w (d − 1, 1) (v, k). One participant seeks links and resources on hypermatrices and hyperdeterminants, specifically methods for developing hyperdeterminants as products of eigenvalues. In quantum information, hyperdeterminants measure quan tum entanglement, under the name “tangle”. our reduction implies that it is hard to tell if four or more qudits are tangled, unless quantum computers can efficiently solve np complete problems. Hyperdeterminant a technically defined extension of the ordinary determinant to ``higher dimensional'' hypermatrices. cayley (1845) originally coined the term, but subsequently used it to refer to an algebraic invariant of a multilinear form. the hyperdeterminant of the hypermatrix (for , 1) is given by.