Math concept, provide insight and discussion, please. I had the thought of a three-dimensional matrix?
Topic: writing a discussion paper
July 21, 2019 / By Gilda Question:
A cube matrix, for example. I realize its not very practical to write or work with on paper... but the concept came to mind of having a single matrix with levels and therefore a third dimensions, with operators and whatnot and its own set of rules.
Oh, I heard of tensors, but didnt know what they were... I didnt know they are a 3-d analogy to matrices. I was always told that matrices are only 2-D. And I guess with tensors in the realm of discussion, matrices are only 2-D after all.
Practical applications? I dont know and I dont care. YOU might NEED a practical use, but I resent the fact you think we all do. Whoever thinks like that is not a mathematician. Dont waste my time with capitalist stupidity.
Best Answers: Math concept, provide insight and discussion, please. I had the thought of a three-dimensional matrix?
Deni | 1 day ago
These are called tensors (or at least they are the notion closest in analogy to a "three-dimensional matrix"), and they can be any number of "dimensions."
Note: it is somewhat misleading to think of them as being dimensional; matrices and tensors in general are just linear combinations of tensor products of vectors and covectors. For them to be truly three-dimensional or higher-dimensional in the same sense that matrices are two-dimensional, there would have to be a dual to a covector space which was something other than the original vector space (but no such thing can be constructed).
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Uh... I hate to be the one to break the news to you, buy 3-D and higher matrices have been used for at least 150 years. There operators and rules are compatible with ordinary 2-D matrices.
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Any ideas for practical applications? I'd be interested to see how you plan on dealing with the operations.
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Originally Answered: One dimensional?
For many years a lot of maths taught was from a very old Geek book called 'The Elements' by Euclid.
He defined a line as "that which has length but no breadth" (or something similar).
It is rather a strange definition but it gives us the image of what a straight line is. It does not exist in our world as you rightly point out it is impossible for us to make one without it having some measurable thickness.
A lot of maths is about pure ideas and concepts which are difficult to reproduce - has anyone ever drawn a perfect circle or a true square if you measured it to the nearest atom?