Matrix exponential by Ciro Santilli 37 Updated 2025-07-16
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.
Video 1.
How (and why) to raise e to the power of a matrix by 3Blue1Brown (2021)
Source.
Elon Musk by Ciro Santilli 37 Updated 2025-07-16
Musk is a truly ambivalent personality. Some points are very good. Some are very bad.
Respect on the technical side by Ciro Santilli.
But the way he treated his first wife Justine Musk, is very very weird, incomprehensible: www.marieclaire.com/sex-love/a5380/millionaire-starter-wife/
Positive Cirocoins for possibly going to reverse Twitter's unfair Trump ban if his Twitter acquisition goes through:
Negative Cirocoins for according to Wikipedia:
Within the merged company [Thiel's Confinity + Elon's X.com], Musk returned as CEO. Musk's preference for Microsoft software over Unix created a rift in the company and caused Thiel to resign.
Video 1.
The REAL Reason Why Tesla Made All Patents Open-Source by The not so boring Man (2021)
Source. Supercut from various interviews/presentations in which Elon saying that Tesla has open source patents and pro open source stuff. Can we trust it? Maybe.
Consider a real valued function of three variables:
Its Laplacian can be written as:
It is common to just omit the variables of the function, so we tend to just say:
or equivalently when referring just to the operator:
DNA detection by Ciro Santilli 37 Updated 2025-07-16
DNA detection means determining if a specific DNA sequence is present in a sample.
This can be used to detect if a given species of microorganism is present in a sample, and is therefore a widely used diagnostics technique to see if someone is infected with a virus.
You could of course do full DNA Sequencing to see everything that is there, but since it is as a more generic procedure, sequencing is more expensive and slow.
The alternative is to use a DNA amplification technique.
Genetics by Ciro Santilli 37 Updated 2025-07-16
High level DNA studies? :-)
Cultured meat by Ciro Santilli 37 Updated 2025-07-16
This is something worth investigating!
Video 1.
Inside the Quest to Make Lab Grown Meat by WIRED (2018)
Source.
Interviews with a few startups in the area, most of the time with Eat Just.
youtu.be/QO9SS1NS6MM?t=217 taught Ciro Santilli something he really appreciated: uncanny valley.

There are unlisted articles, also show them or only show them.