Ciro Santilli @cirosantilli 37

 Articles (11k) Discussions (26) Comments (64) Follows  Received likes Files

New Updated  Top  Announced  A-Z  Liked  Followed

Lie bracket of a matrix Lie group Updated 2025-07-16

[X, Y] = X Y - Y X

(1)

This makes it clear how the Lie bracket can be seen as a "measure of non-commutativity"

Because the Lie bracket has to be a bilinear map, all we need to do to specify it uniquely is to specify how it acts on every pair of some basis of the Lie algebra.

Then, together with the Baker-Campbell-Hausdorff formula and the Lie group-Lie algebra correspondence, this forms an exceptionally compact description of a Lie group.

 Read the full article

Marijuana Updated 2025-07-16

 Read the full article

Meter Updated 2025-07-16

 Read the full article

Mt. Gox Updated 2025-07-16

 View more

The first Bitcoin exchange. Coded as a hack, and they didn't manage to fix the hacks as the site evolved in a major way, which led to massive hacks.

Their creation is clearly visible on the archive history of bitcoin.org: web.archive.org/web/20100701000000*/bitcoin.org which started having massively more archives since Mt. Gox opened.

Video 1.

One Mistake Brought Down This FBI Most Wanted Hacker by Crumb (2023)

Source. Good overview of Mt. Gox.

 Read the full article

One parameter subgroup Updated 2025-07-16

 View more

The one parameter subgroup of a Lie group for a given element

M

of its Lie algebra is a subgroup of

G

given by:

e^{tM} \in G ∣ t \in R

(1)

Intuitively,

M

is a direction, and

t

is how far we move along a given direction. This intuition is especially vivid in for example in the case of the Lie algebra of

SO (3)

, the rotation group.

One parameter subgroups can be seen as the continuous analogue to the cycle of an element of a group.

 Read the full article

Piezoelectric motor Updated 2025-07-16

 Read the full article

The best technology YouTube channels Updated 2025-07-16

 Read the full article

You can learn more from older students than from faculty Updated 2025-07-16

 View more

Wikipedia mentions quoting his Nobel Prize biography:

In Monod's studies he discovered that the course work was decades behind the current biological science. He learned from other students a little older than himself, rather than from the faculty.

 Read the full article

Cyc Updated 2025-07-16

 Read the full article

FTX Updated 2025-07-16

 Read the full article

Imperial College London Updated 2025-07-16

 View more

Nice, nice place. Natural sciences only, no bullshit.

 Read the full article

ITER Updated 2025-07-16

 Read the full article

LevelDB Updated 2025-07-16