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It's basically duck-typing. If you can do arithmetic on it, it's a number. If you can do matrix operations, it's a matrix. If it satisfies the axioms of X, it's an X.



Not true. You can do arithmetic on many things that are not a number. This is why objects such as "rings" exist.

Matrix is not defined just by operations like a ring is, but also by structure - you have N independent axes in a specified space.


That's a bit pedantic but sure. Here it is fixed:

> If you can do numeric arithmetic on it, it's a number.


That is begging the question. What does "numeric" mean?


Do you have a definition of number that addresses this?

>you have N independent axes in a specified space.

Only if you have an operation that maps the matrices to that space.




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