Let[Ctilde](s)[Dtilde](s)−1be a right coprime matrix fraction description of the (r × m) strictly proper transfer function matrixT(s) of a linear multivariable system Σ = (A, B, C). In this paper we establish a direct relation between (i) the algebraic concept of a right divisorCR(s) of the ‘numerator’ matrix[Ctilde](s), i.e. a (not necessarily square) polynomial matrixCL(s) that satisfies:[Ctilde](s) =CL(s)CR(s) for some polynomial matrixCL(s), and (ii) the geometric concept of an (A, B)-invariant subspace which is contained in the kernel ofC. A special class of right divisorsCR(s) ofC(s) which correspond to (A, B)-invariant subspaces in kerCis characterized by a number of properties and a simple formula is presented which expresses the above correspondence. By generalizing the concept of a greatest right divisor (GRD) of a polynomial matrix to include also possibly non-square polynomial matrices, it is shown that GRDs of the numerator matrixC(s) correspond to the maximal (A, B)-invariant subspace in kerC.