Ciro Santilli @cirosantilli 35

Cardinality $\le$ dimension of the vector space.

en.wikipedia.org/w/index.php?title=Nutrient&oldid=1075972831#Essential gives somewhat of an overview:

Formal name: "fungi".

For a quick and dirty introduction to the format, see: ELF Hello World Tutorial.

Deterministic, but non-local.

Formal name: "plantae".

Given stuff like arxiv.org/pdf/2107.12475.pdf on Erdős' conjecture on powers of 2, it feels like this one will be somewhere close to computer science/Halting problem issues than number theory. Who knows. This is suggested e.g. at The Busy Beaver Competition: a historical survey by Pascal Michel.

math.stackexchange.com/questions/41706/practical-uses-of-matrix-multiplication/4647422#4647422 highlights deep learning applications.

A little suspicious that it bears the name of Lorentz, who is famous for special relativity, isn't it? See: Maxwell's equations require special relativity.

Measured particle speeds with a rotation barrel! OMG, pre electromagnetism equipment?

Like everything else in Lie group theory, you should first look at the matrix version of this operation: the matrix exponential.

The exponential map links small transformations around the origin (infinitely small) back to larger finite transformations, and small transformations around the origin are something we can deal with a Lie algebra, so this map links the two worlds.

The idea is that we can decompose a finite transformation into infinitely arbitrarily small around the origin, and proceed just like the product definition of the exponential function.

The definition of the exponential map is simply the same as that of the regular exponential function as given at Taylor expansion definition of the exponential function, except that the argument $x$ can now be an operator instead of just a number.

Examples: