Determinants of multi-dimensional matrices

Hi there. I study Electrical Engineering (first year), and I am being
bothered by by Linear Algebra issues lately. One of them is the
three-(or more)-dimensional matrices. In Linear Algebra lessons, we
only have to deal with two-dimensional matrices, but, in fact, there is
no limitation in the number of dimensions, it could be anything. Yet,
all definitions we have learnt are designed for two-dimensional
matrices. One of them is the determinant. I am trying to discover on my
own, how to compute the determinant of a NxNxN matrix, but I am
baffled. Maybe I should ask if there IS such a thing as determinant of
a three-dimensional matrix.

Another one is the multiplication of three-dimensional matrices. All
clear on how to multiply an MxN with an NxK matrix. But what about
three dimensional matrices? No clue at all...

Tero

.

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