I'm wondering if he's hoping to replace the array data in the pre-compiled library with data from the header file included in the library-using program. That won't work. You could make the library's array extern and define the actual array in the user code. (In this case there's no "default" and the array must be in the user code, even if it is the default.)
Library header file:
Code:
extern const float scaling[5][5]; // externally defined object
User-code header file:
Code:
const float scaling[5][5] = {
    { 0.2, 0.2, ... },
    { 0.2, 0.2, ... },
    ...
};