I'm not definate on what a matlab is. Does it contain only the materials properties, ie. spec/glossiness/IOR, and you would also input a separate map?
AFAIK it is a file used by autodesk. Does this mean that the same .mat file could be used with different renderers in 3ds max (MR, Vray)?
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Matlab is a mathematics app that happens to save files with the same extension.
.mat is a package, like lets say rar or zip, that contains max materials.
an excellent way to store, organize and share your materials.
Mind you, it will not contain textures and the materials will expect to find the textures at the same path. For organized studios that store their textures in central location this would not be a problem.
You can save or load these files when you click on "Get Material" at the material editor then on your left enable mtl Library and options such as open merge etc become available.
I use .mat files as palettes when i expect to have a large amount of materials in my scene or when i create generic materials that are reusable.
You can also load materials from the same menu straight from a max file which can be used also as an alternative or other formats. but .mat is clean and light.
This way you can have as many materials as you need available at any time and perhaps better organized than a nodal interface.
Regarding matlab the software, it was used to generate shaders for mR and renderman.
of course this was not what it is designed to do, but, it has a tool that visually represents complex mathematical functions.
It was quite popular in the past before slim etc become available.