Autocommands for Matlab in vim?

Question

I use several different programming languages every day, and I'd like to have different tab widths (in spaces) for each. For example: I use the "standard" 2 spaces for Ruby, but all our existing Matlab code uses 4 spaces.

I have this from my personal ~/.vimrc:

augroup lang_perl
    au!
    set tabstop=4 " tabstop length N in spaces
    set shiftwidth=4 " make >> and friends (<<, ^T, ^D) shift N, not the default 8
    set expandtab " Use spaces instead of tabs
augroup END

augroup lang_ruby
    au!
    set tabstop=2 " tabstop length N in spaces
    set shiftwidth=2 " make >> and friends (<<, ^T, ^D) shift N, not the default 8
    set expandtab " Use spaces instead of tabs
augroup END

Those work, but the following doesn't:

augroup lang_matlab
    au!
    set tabstop=4 " tabstop length N in spaces
    set shiftwidth=4 " make >> and friends (<<, ^T, ^D) shift N, not the default 8
    set expandtab " Use spaces instead of tabs
augroup END

I really don't understand how augroup lang_ruby figures out that I'm editing a Ruby file. (My searches brought up ftdetect, but the solution wasn't obvious.) It doesn't seem like vim knows that I'm editing Matlab using augroup lang_matlab. What do I change to make this work?