I've been reading around that matrices (for example, rotation matrices, but not only) can be thought somehow as coordinate systems. My question is: how is that possible? I've seen for example that if we're using row-major conventions, the rows of the matrices involved in the transformations (specifically I've seen about rotations) can be thought as the vectors representing some coordinate system (specifically it should be a local coordinate system).Why is this the case? And why specifically a local coordinate system? What does it even mean local coordinate system in this context? Are there any other type of matrices, apart from the rotation matrices, which can be thought as coordinate systems? If yes, which ones, and why?Matrices usually represent a transformation (linear or not, maybe also affine in computer graphics), but it's new to me to think about matrices as coordinate systems. 
How is that possible that matrices can be thought as coordinate systems?
transformations;matrices;affine transformations