## Hyperdeterminacy Blog Index

**Hyperdeterminants****Hyperdeterminant Definition****The Determinant is a Hyperdeterminant of a Matrix****Cayley’s Hyperdeterminant****Hyperdeterminants and Elliptic Curves I****Hyperderminants as Invariants****Unpopularity of Hyperdeterminants According to Google****The Hyperdeterminant Book****Hyperdeterminants and The Levi-Civita Symbol****Hyperdeterminants and Discriminants****Discriminants as Invariants****Quartic Discriminants****Hypermatrix Diagonalisation****Schläfli’s Hyperdeterminant****Hyperdeterminants and Elliptic Curves II****Boundary Format Hyperdeterminants****The Degree of Hyperdeterminants****Multiplicative Hyperdeterminants****Hypermatrix Inverses****Diophantine Quadruples****Cayley’s Hyperdeterminant and Principal Minors****Diophantine Quadruples and Symmetric Matrices****A Symmetric Hypermatrix and Brahmagupta’s Formula****Update on Popularity of “Hyperdeterminant”**

Advertisements

June 11, 2009 at 5:17 am

Regarding “Hypermatrix Inverses”, which is very interesting. If A and X are hypercubes of format m^r, and we should solve AX = I which is of format m^2, where the r directions of A and X are identified, and r-1 contracted in the product, then this is a set of rm^2 linear equations in m^r variables X. So if there is a solution there will be a large space of solutions if r < m^(r-2). It should be possible to calculate the exact rank of the generic solution space of AX = I. First one should solve AX = 0, the null space. When r = 3 it should be interesting.

June 11, 2009 at 8:58 am

DG’s comment has been copied to the “Hypermatrix Inverses” post so replies can go there.