Ciro Santilli @cirosantilli 35

Two are riculously well known:

A way to defined geometry without talking about coordinates, i.e. like Euclid's Elements, notably Euclid's postulates, as opposed to Descartes's Real coordinate space.

Given a matrix $A$ with metric signature containing $m$ positive and $n$ negative entries, the indefinite orthogonal group is the set of all matrices that preserve the associated bilinear form, i.e.:Note that if $A=I$, we just have the standard dot product, and that subcase corresponds to the following definition of the orthogonal group: Section "The orthogonal group is the group of all matrices that preserve the dot product".

As shown at all indefinite orthogonal groups of matrices of equal metric signature are isomorphic, due to the Sylvester's law of inertia, only the metric signature of $A$ matters. E.g., if we take two different matrices with the same metric signature such as:and:both produce isomorphic spaces. So it is customary to just always pick the matrix with only +1 and -1 as entries.

The non-regular version of the hypercube.

As of 2020, no one knows how to build the major desktop distros fully from source into the ISO, and especially so in a reproducible build way. Everything is done in build servers somewhere with complicated layers of prebuilds. It's crap.

See also: cirosantilli.com/linux-kernel-module-cheat/#linux-distro-choice

Yes:

No:

Most notable example: $L^2$.