Ndtyhij

Is there a list of the symbols shown in "The Matrix" when operators do they work watching it? How many are they? What are their names? Which ones didn't exist by the time the movie was shot?

As explained in the answer to this closely related question, all of those symbols are "real" characters, they've just been flipped horizontally to mirror images of themselves. If you look at a still image flipped back, it's easier to tell:

The top is from the movie, the bottom is the same shot mirrored left-to-right. You can tell that many of the symbols are just normal Latin alphabet digits, letters, and symbols. The rest are Japanese characters (mostly half-width katakana, though there's at least one kanji in there as well). None of them were created specifically for the movie.

So I was curious myself so watched the opening of the first film frame by frame in mirror mode and noted down what I saw. That being the case there is probably some missing.

Notably, there is no 6 and the only Kanji I found is 日 (roughly meaning day/sun). The only roman letter is Z until the title appears in which case letters in "THE MATRIX" appear. Most of the symbols are Katakana, however they are not uniformly distributed. Some appear very frequently while others are completely absent.

Identifiable symbols (all are mirror versions unless noted)

• Kanji: "日"


• Katakana: "ﾊﾐﾋｰｳｼﾅﾓﾆｻﾜﾂｵﾘｱﾎﾃﾏｹﾒｴｶｷﾑﾕﾗｾﾈｽﾀﾇﾍ"


• Missing Katakana: "ｦｲｸｺｿﾁﾄﾉﾌﾔﾖﾙﾚﾛﾝ" (at least I couldn't find them)


• Numbers: "012345789", "3" is upside down, "4" has underscore, "7" is not mirrored


• Roman: "Z" only, then "THEMATRIX" for the title.


• Punctuation/Arithmetic: ":・."=*+-<>"


• Other: "¦｜" and dashed underscore (╌ but lower down)


• Unknown: Somethine like ç and something like ﾘ but with an overbar (might be ｸ).

In total that's around 67 characters.

These are mostly known characters, but they are flipped (mirrored). They include Arabic digits, Latin letters, punctuation/math/etc characters, Kanji and halfwidth Katakana.
Here you are, a list (I believe it's 100% full) from analyzing the code rain in opening scene (0:30-0:37) and dream scene:

ARABIC DIGITS

• mirrored: 2, 5, 9, 8 (two identical circles – hard to tell if mirrored)
  


• not mirrored: 1, 7 (without the line crossing through the middle), 0 (a "slashed zero" form), 3 (a "flat-topped three" form, upside down), 4 (a "closed top four" form, with underscore, but see )
  


• *) there is no 6
  

LATIN LETTERS (NOT MIRRORED)

• Z (sans-serif)
  


• *) +(letters AEHIMRTX at the end of intro forming "THE MATRIX", but it's clearly visible that they were added to the video after generating the code rain because they misalign, glow brighter, are thinner and have serif font-face)
  

PUNCTUATION/MATH/ETC.
(symmetrical, so no sense saying if mirrored)

• :."=*+-¦|_
  


• [space] (I assume so; sometimes there is an empty place in a column and one could treat that as blank place, not [space] generated; but sometimes it really appears in a sequence in spots where the symbols change frequently)
  


• ╌ (← "double dash horizontal" but low, on the bottom line, like underscore; I haven't found such glyph in Unicode table and online)
  


• *) there's no dot in the middle of the text line (・/∙/•/etc.) (as Annan stated) – it's rather normal full stop [.], because it's on the bottom
  

(MOST OF) HALF-WIDTH KATAKANA (MIRRORED) (in order of appearance in Unicode table)

• ｦｱｳｴｵｶｷｹｺｻｼｽｾｿﾀﾂﾃﾅﾆﾇﾈﾊﾋﾎﾏﾐﾑﾒﾓﾔﾕﾗﾘﾜ
  


• missing ones: ｲｸﾁﾄﾉﾌﾍﾖﾙﾚﾛﾝ
  


• *) Annan said that character [ﾍ] is present in code – I believe he was wrong; I think he must've seen a fragment of another character during appearing (they appear not each at once but each unhiding from top to bottom)
  


• **) what's interesting – [ｳｵｹ] are with overscore, [ﾈﾎﾔ] are with underscore; I think this is somewhat because of emulating technical problems of old screens; just like the underscore in digit [4]
  

KANJI

• 日