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What is matrix mxing?

Matrix mixing may sound complicated but it's a very simple and powerful thing.

Using matrix mixing you can specify an audio channel how loud to appear on a specified output channel.
For an example:
           |    |     |
           V    V     V
         Left Right Center
<-Left   1    0     0
<-Right  0    1     0
<-Center 0    0     1
You can notice the diagonal '1's. A diagonal matrix always means 'no change', every channel is played on the same output as was input.
You can read the matrix like this: Read the top (input) column: Left in - then the row: left output value is '1' (full). So that this means the left in channel is played at full volume on left out channel.
Then the second column: right in, take the first row left out is 0. So the right in channel is not played on the left output. Etc.
Here's an example on swapping the left-right channels for output:
           |    |     |
           V    V     V
         Left Right Center
<-Left   0    1     0
<-Right  1    0     0
<-Center 0    0     1
Now left is silent '0' on left out and full volume '1' on right. Center is not affected.

The values are floating point values where '1' means full volume, '0' means silent, so you can use for example '0.5' to play at half volume on that channel.
It is advised to always keep the sum of a horizontal row at max. '1'. If you take a look at the 2 matrices both have always horizontally sum of '1'. If the sum is greater than '1' then that will mean that the row (output channel) is possible to clip. No problem if working in 32 bit float mode you just have to normalize the audio file when encoding/saving it.