Ciro Santilli @cirosantilli 37

The most important example is perhaps $SO(3)$ and $SU(2)$, both of which have the same Lie algebra, but are not isomorphic.

Show up when solving the Laplace's equation on spherical coordinates by separation of variables, which leads to the differential equation shown at: en.wikipedia.org/w/index.php?title=Legendre_polynomials&oldid=1018881414#Definition_via_differential_equation.

We can almost reach the Lie algebra of any isometry group in a single go. For every $X$ in the Lie algebra we must have:because $e^{tX}$ has to be in the isometry group by definition as shown at Section "Lie algebra of a matrix Lie group".

Then:so we reach:With this relation, we can easily determine the Lie algebra of common isometries:

Bibliography:

Unit of electric current.

Affected by the ampere in the 2019 redefinition of the SI base units.

A series of systems usually derived from the International System of Units that are more convenient for certain applications.

Before we get a decent open source integrated development environment, what else can you do?

But also perfect for small one-off files when you don't have the patience to setup said IDE.

vim's defaults are atrocious for the 21st century! Vundle is reasonable as an ad-hoc package manager, but it can't set fixed versions of packages:

Represents image pixel by pixel, rather than by mathematical primitives such as done in vector graphics:

The opposite of a human-readable format.

The simplest harmonic oscillator system.