Some complex phenomenons are described as a multidimensional equation systems. To solve the corresponding equation systems we need to compute the hyperdeterminant at the first step. Is there any algorithm to compute the hyperdeterminant for an (n,m ,p) system?
see in Section 14.3 of the book:
“Discriminants, resultants, and multidimensional determinants ”
by Gelfand-Kapranov-Zelevinsky.
This is a good question.
In addtion to an incisive already given by @Romeo Rizzi, consider
C. Castro, The large N limit of exceptional Jordan matrix models and M, F theory:
http://www.rxiv.org/pdf/0908.0089v1.pdf
Formula (2.6), page 11, provides a hyperdeterminant defined in terms of a cubic matrix. See, also, the discussion about hypedeterminants on page 4 in
C. Castro, A unified description of particles, strings and branes in Clifford spaces and p-brane/polyparticle duality, Clark Atlanta University, 2014:
http://vixra.org/pdf/1501.0051v1.pdf
as well as
A. Miyake, Physics Review A 67, 2003, no. 012108
A. Miyake, F. Vertraete, Physics Review A 69, 2004, no. 012101
A. Miyake, H.J. Briegel, Physics Review A 95, 2005, no. 220501
Miyake's hyperdeterminants are discussed in
R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki, Quantum entanglement, arXiv 0702225v1, 2007:
http://cds.cern.ch/record/1021525/files/0702225.pdf
Continuing this discussion, research papers by Michal Kordecki and Karol Hordecki are on RG:
https://www.researchgate.net/search.Search.html?origin=ac&query=Horodecki
Professor James ;
Thank you so much for the valuable references you gave;
In our research laboratory we have designed a parallel computational model having a hypercubic topology. I believe that this topology fits very well to the hypercubic problems.
My goal is to find or establish a hypercubic matrix equation to model a complex systems.
the solution of this problem is obviously well suited to the designed hypercubic machine with a fastest runtime.
a ( 2 x 2 x 2) matrices are on test.
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