Ciro Santilli @cirosantilli  40

The most powerful GUI file manager ever?? Infinite configurability??

Ciro Santilli wasted some time on it before he gave up on file managers altogether and started using only the CLI with a few aliases.

Ciro Santilli considered it before he stopped using file managers altogether, it is not bad.

GitHub account: github.com/hplgit

It should be mentioned that when you start Googling for PDE stuff, you will reach Han's writings a lot under his GitHub Pages: hplgit.github.io/, and he is one of the main authors of the FEniCS Project.

Unfortunately he died of cancer in 2016, shame, he seemed like a good educator.

He also published to GitHub pages with his own crazy markdown-like multi-output markup language: github.com/hplgit/doconce.

Rest in peace, Hans.

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:

The differential equation that is solved by the exponential function:with initial condition:

TODO find better name for it, "linear homogenous differential equation of degree one" almost fully constrainst it except for the exponent constant and initial value.

Is the solution to a system of linear ordinary differential equations, the exponential function is just a 1-dimensional subcase.

Note that more generally, the matrix exponential can be defined on any ring.

The matrix exponential is of particular interest in the study of Lie groups, because in the case of the Lie algebra of a matrix Lie group, it provides the correct exponential map.

This is how you transform the Lagrangian into the Hamiltonian.