Ciro Santilli @cirosantilli 35

Since rat and mouse are not scientifically specific names, we'll just use them interchangeably.

When one specific species is implied, we will mean Mus musculus by default.

If any of you ever read this, do send me an email to Ciro Santilli saying hi and we can agree on a clear separation of usernames.

Although if you are just starting out, maybe you should just go from scratch with a unique Internet alias.

A younger unrelated Argentinian homonym who likes soccer that can be found through Google:Ciro used to like playing soccer too! :-)

www.ancestry.com.au/genealogy/records/ciro-santilli-24-bkmssg documents a "Ciro Santilli" born 31 Jan 1887 at Castelvécchio in Subéquo, L'Aquila, in the Abruzzo region, just like Ciro Santilli's ancestors. Parents Francesco Santilli and Anna Silveri. The page also mentions:

Unknown:

Decent encyclopedia of mathematics. Not much motivation, mostly statements though.

Created by:

Unlike Wikipedia, they have a more sane forum commenting system, e.g. a page/forum pair:

This was the first generation of commercially successful radios.

It uses a crystal detector as its diode, which is a crucial element of the radio, thus its name.

They were superseded by transistor radios, which were much more reliable, portable and could amplify the signal received.

This one took a while! Major developments were from the 70s! Perhaps it took the Internet revolution to make its importance clear.

Founder: Peter Armstrong

The general idea is publishing entire books with usual copyright, but with gradual updates.

ruboss.com/ documents their stack, a somewhat similar choice to OurBigBook.com as of 2021, notably Next.js. But backend in Ruby on Rails. They actually managed Apollo/GraphQL, which Ciro Santilli would have liked, but din't have the patience for.

The founder/CEO Peter Armstrong www.linkedin.com/in/peterburtonarmstrong/ He looks like a nice guy.

A linear map is a function $f:V_1(F)\to V_2(F)$ where $V_1(F)$ and $V_2(F)$ are two vector spaces over underlying fields $F$ such that:

A common case is $F=\mathbb{R}$, $V_1={\mathbb{R}}_m$ and $V_2={\mathbb{R}}_n$.

One thing that makes such functions particularly simple is that they can be fully specified by specifyin how they act on all possible combinations of input basis vectors: they are therefore specified by only a finite number of elements of $F$.

Every linear map in finite dimension can be represented by a matrix, the points of the domain being represented as vectors.

As such, when we say "linear map", we can think of a generalization of matrix multiplication that makes sense in infinite dimensional spaces like Hilbert spaces, since calling such infinite dimensional maps "matrices" is stretching it a bit, since we would need to specify infinitely many rows and columns.

The prototypical building block of infinite dimensional linear map is the derivative. In that case, the vectors being operated upon are functions, which cannot therefore be specified by a finite number of parameters, e.g.

For example, the left side of the time-independent Schrödinger equation is a linear map. And the time-independent Schrödinger equation can be seen as a eigenvalue problem.