We introduce Recursive Matrix Systems (RMS) which encompass mildly context-sensitive formalisms and present efficient parsing algorithms for linear and context-free variants of RMS. The time complexities are 𝒪(n^{2h + 1}), and 𝒪(n^3h) respectively, where h is the height of the matrix. It is possible to represent Tree Adjoining Grammars (TAG [1], MC-TAG [2], and R-TAG [3]) as RMS uniformly.