I’m just being silly, but I mean that if everything can be represented as a matrix then there’s a point of view where things like complex numbers are just “names” of specific matrices and the rules that apply to those “names” are just derived from the relevant matrix operations.
Essentially I’m saying that the normal form is an abstract short hand notation of the matrix representation. The matrices are of course significantly harder and more confusing to work with, but in some cases the richness of that structure is very beautiful and insightful.
(I’m particularly in love with the fact one can derive spinors and their transforms purely from the spacetime/Lorentz transforms. It’s a really satisfying exercise and it’s some beautiful algebra/group theory.)
I’m just being silly, but I mean that if everything can be represented as a matrix then there’s a point of view where things like complex numbers are just “names” of specific matrices and the rules that apply to those “names” are just derived from the relevant matrix operations.
Essentially I’m saying that the normal form is an abstract short hand notation of the matrix representation. The matrices are of course significantly harder and more confusing to work with, but in some cases the richness of that structure is very beautiful and insightful.
(I’m particularly in love with the fact one can derive spinors and their transforms purely from the spacetime/Lorentz transforms. It’s a really satisfying exercise and it’s some beautiful algebra/group theory.)