What is a "static" function in C?

The question was about plain c functions, not c++ static methods, as clarified in comments.

I understand what a static variable is, but what is a static function?

And why is it that if I declare a function, let's say void print_matrix, in let's say a.c (WITHOUT a.h) and include "a.c" - I get "print_matrix@@....) already defined in a.obj", BUT if I declare it as static void print_matrix then it compiles?

UPDATE Just to clear things up - I know that including .c is bad, as many of you pointed out. I just do it to temporarily clear space in main.c until I have a better idea of how to group all those functions into proper .h and .c files. Just a temporary, quick solution.

Answer

static functions are functions that are only visible to other functions in the same file (more precisely the same translation unit).

EDIT: For those who thought, that the author of the questions meant a 'class method': As the question is tagged C he means a plain old C function. For (C++/Java/...) class methods, static means that this method can be called on the class itself, no instance of that class necessary.