if you don't believe that side=L-R, download this http://www.brainworx-music.de/en/plugins/bx_solo free plugin from Brainworks and compare the results. or if you use Live, you can do LR to MS transformation with two utilities and an effect rack. set the stereo width (maybe it's called otherwise) parameter of one utility to 0% (Mid or mono) and the other to 200% (sides)...
Subtracting L from R is the same as adding L to a polarity-inverted R. Yes, it is to do with phase, but only regarding a 180degree shift for all frequencies, which is the same as a polarity inversion, which is the same as multiplying an audio stream by -1, hence just subtracting them does work ... no?
The only similar kind of matrix that I know of is the Gerzon 2-3 matrix, which attempts to separate stereo l/r into 3-channel mid/left/right. It uses ms encoding/decoding, but it isn't the same.
"Side" is only two channels when it is mixed with the mid signal (even though that still doesn't make sense :p ) ... have you ever use an m/s mic array? It's the exact same concept, the "side" signal comes from a bidirectional microphone because the two lobes of the polar pattern are mechanically 180degrees out of phase with each other (opposite polarity).
I also would like to see working patch, and I've got some more questions:
Do you know some sound processing techniques especially dedicated for M/S which are more complicated than playing with loudness and Eq? For example mentioned brainworx M/S plugin is really awesome. Do you know what it does with side signal?
I have no idea what they do with their MS algorithms-- maybe as a total guess they make the mid bassier or something. I'm not at all familiar with their plugins.
to quote brainworx own marketing:
"bx_meter is not the tool that will automatically make your mixes sound better, of course, but it will give you some insight in what you are doing when you are mixing or mastering, and understanding the correlation of dynamics, M/S, phase and levels by listening to your music will help you mix / master better."
In other words all ms processing really allows you to do is change the stereo spread as implemented in this patch: (of course you can do anything you like with the M and S signals before re-encoding into stereo, but that's up to you)
"Do you know some sound processing techniques especially dedicated for M/S which are more complicated than playing with loudness and Eq? For example mentioned brainworx M/S plugin is really awesome. Do you know what it does with side signal?"
definetly a limiter or gate are just as cool as compressors, but it can be fun with reverb, too.