Definition of matrix_world

I would like a precise definition of matrix_world and the other matrices.

If I’m not wrong, we consider the frame R1 with axis parallels to the original frame and with origin in the 3D cursor. We consider the frame R2 of the object O. There is a unique orthogonal transformation sending R1 to R2. This extends to a linear transformation T of the projective space and O.matrix_world is the matrix of T.

Is it correct ? If not, what is the definition ?

Similarly, I would like to know the definitions of matrix_local, matrix_basis and matrix_inverse_parent in a mathematical unambiguous language if possible.

Thanks in advance.

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The best you are going to get is this:

Though it sounds like you know enough about linear algebra and how it applies to 3D math to correctly interpret the descriptions.

You are correct about the usage of Object.matrix_world. It transforms points in the Object space into World space.