Tuesday, October 13, 2009


The concept of hyperdeterminant is as new to me as a few days and is introducing me into a fascinating new branch of algebra that I did not even suspect. I am very familiar with tensors and how they can be seen as multidimensional arrays that generalize matrices, but the concept of hypermatrices goes further.

The hyperdeterminant was invented (discovered) by the famous mathematician Cayle, who gave us many things including the Cayle transform, useful to approximate the exponential of anti-Hermitian matrices, and the amazing Cayle-Hamilton theorem of linear algebra.

There is active research today and I even found a blog

More recently I found that Thomas Wolf and Sergey Tsarev are implemening serious computer work in order to find hyperdeterminants of higher order
Hyperdeterminants as integrable discrete systems.

What I had in mind was the hypertederminant of at least 5x5x5 cubic matrices, but now I known this is an exceedingly difficult problem. Now my question is if there is one way to find a good approximation.

MMM,.... I just, learned about other alternative definitions of hyperdeterminants, so the possibilities are still open.

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