Ciro Santilli @cirosantilli 35

Given a linear operator $A$ over a space $S$ that has a inner product defined, we define the adjoint operator $A^{†}$ (the $†$ symbol is called "dagger") as the unique operator that satisfies:

Most commonly refers to: exponential map.

You could put an LED in a cavity with a thin long hole but then, most rays, which are not aligned with the hole, will just bounce inside forever producing heat.

So you would have a very hot device, and very little efficiency on the light output. This heat might also behave like a black-body radiation source, so you would not have a single frequency.

The beauty of lasers is the laser cavity (two parallel mirrors around the medium) selects parallel motion preferentially, see e.g.: youtu.be/_JOchLyNO_w?t=832 from Video "How Lasers Work by Scientized (2017)"

Others:

DokuWiki about physics, mostly/fully written by Jakob Schwichtenberg and therefore focusing on particle physics, although registration might be open to all.

This important and common simple case has easy properties.

Specials sub case of the general linear group when the determinant equals exactly 1.

All possible repetitive crystal structures!

219 of them.

This is a good book, it gives a summary of biographies, and a reasonable description of the main ideas, with many illustrations. Each subject is not presented in incredible detail, but it is a good overview of events.