Yes, but does that profile represent the raw data’s actual colorspace?
I have quite a few profiles for my Nikon D7000 now, including two matrix profiles made from different targets, one from a ColorChecker Passport with 24 patches, another from a Wolf Faust IT8 targer, with 128 patches. Here are their primaries, extracted with exiftool:
CC24:
Red Matrix Column : 0.78865 0.34801 0.05725
Green Matrix Column : 0.07399 0.82153 -0.28322
Blue Matrix Column : 0.09937 -0.1787 1.0423
IT8:
Red Matrix Column : 0.74454 0.30803 0.0374
Green Matrix Column : 0.14598 0.86247 -0.19815
Blue Matrix Column : 0.07367 -0.17049 0.98566
Similar, but not identical. So, which one represents the raw data ‘colorspace’?
A target-sourced camera profile represents a transform that makes colors from a particular camera that are consistent to the reference values for that target. For other images, linear interpolation fills in the cracks, but anchored to those 24 or 128 reference values. In the writings of the ‘big heads’ on this topic, I’ve seen such matrices referred to as ‘compromise matrices’, for this very reason.
Camera profiles are a well-misunderstood mechanism, with all the various devices they contain (don’t get me going about ‘look’ profiles… 
). What is not-well recognized is their fundamental role to provide the starting point for the color management chain of transforms to eventually something that can be rendered so we like it. But that starting point is a contrivance, not based on some intrinsic aspect of the light measurements but instead based on some external reference point like a target. Even spectral sensitivity-based profiles involve the creation of a ‘virtual target’ to feed the profile generation logic.
So, while a camera profile represents a notion of a colorspace that can be used to transform raw data to something anchored in a colorimetrically-representative reference like CIE_1931 XYZ, none of then can be considered to be the definition of the raw data’s One True Colorspace, in the same manner sRGB primaries represent the bounds of a sRGB-encoded image…