Are Cube Matrices the Next Frontier in Linear Algebra?

[Vorde]

I just had my last Linear Algebra class, and I didn't get a chance to ask the one question that has been bugging me ever since we started in earnest with matrices.

Why aren't there cube matrices? I mean, mathematical entities where numbers are 'laid out' in 3d not in 2d (not quite mathematically rigorous, but you get the idea). Obviously one could do this with successive matrices, but I wonder if more is to be gained by studying this object as a whole.

Is this a thing? Is there an obvious reason I'm missing as to why there is nothing to gain by doing this?

 

[pbuk]

There are, and they certainly are useful; physics wouldn't have got much beyond Newton without them. Google "tensors".

 

[Vorde]

Huh, you know I've known about tensors for a while but in a purely pop-science way (the only actual tensors I've been exposed to were in a five-minute digression by my teacher briefly explaining them), I hadn't ever been told to think of them that way!

 

[pbuk]

That's a shame, although you have actually been exposed to tensors for some time. Ordinary numbers (scalars), vectors and matrices are just special cases of tensors with 0, 1 and 2 dimensions respectively.