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”
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.