Re: Determinants of multi-dimensional matrices

Hi - I recently did a search on the topic of "determinant of a
n x n x n matrix", which was separately posted in this NG.
That one was motivated by the search for invariants of a 3-tensor,
as described there. In our Math-Physics library I found something:

> Found a determinant rule for "higher class matrices" in Chapter XXIV
> of Muir's "A Treatise on the Theory of Determinants", Dover, 1928.
> "Class" is defined there as number of dimensions of the matrix =
> number of indices in the entries. My problem is of class 3.

> According to Muir, Cayley (the inventor of matrix algebra) gave a
> determinant rule valid for even classes in 1843. An odd-class rule
> was proposed by Scott (another Englishman) in 1879. The number
> of terms for a n x n x ... n (k dimensions) Cayley-Scott
> determinant is (n!)^(k-1)

Muir's chapter also discusses multiplication rules. There are
additional pre-1928 references given there but dont seem
easily accessible. Paul Abbott graciously posted a link to a
more recent paper in a follow-up to the other post.

.

Relevant Pages

  • Re: Determinants of multi-dimensional matrices
    ... > One of them is the determinant. ... > Found a determinant rule for "higher class matrices" in Chapter XXIV ... Higher Dimensional Determinants, Advances in Mathematics, v121, ... 1996, 167-195, which has some post-1928 references. ...
    (sci.math)
  • Re: Onto Hersteins topic in Algebra
    ... >Using a Cayley table I could see if this is a group. ... Given any nonzero first row, how many second rows would make the ...
    (sci.math)