We established a novel semisimple commutative algebra called t-algebra, which is backward-compatible to the field of complex numbers. Many notions of complex numbers and matrices are generalized. The notion of metric space is generalized. We even believe we can generalize the notion of manifolds in a straightforward backward-compatible manner.
We contend that the magnificent edifices of data analytics, machine intelligence, and beyond should have been built over the t-algebra rather than the classical simple algebra (i.e., the field of complex numbers). We have open-sourced our MATLAB functions at the following URL. https://github.com/liaoliang2020/talgebra
A detailed document for the code repository is now in preparation. Is there someone interested in rewriting those functions to a Python version?
As far as I know, Hamilton’s quaternions and other hypercomplex numbers in Clifford algebra are efforts to generalize complex numbers. However, they are either non-commutative or non-Euclid-like. I think commutativity and Euclid-likeness are probably critical in generalized data analytics. Whether there are some existing commutative algebras of generalized scalars and generalized matrix paradigms over them? If any, I would like to know more of them.
Big thanks.
