Matrix string theory
In physics, Matrix string theory is a set of equations that describe superstring theory in a non-perturbative framework. Type IIA string theory can be shown to be equivalent to a maximally supersymmetric two-dimensional gauge theory, the gauge group of which is U() for a large value of N. This Matrix string theory was first proposed by Luboš Motl in 1997  and later independently in a more complete paper by Robbert Dijkgraaf, Erik Verlinde, and Herman Verlinde. Another matrix string theory equivalent to Type IIB string theory was constructed in 1996 by Ishibashi, Kawai, Kitazawa and Tsuchiya. This version is known as the IKKT matrix model.
M(atrix) Theory 
M(atrix) theory (also known as BFSS-Matrix theory) is a fundamental formulation of M-theory as a random matrix model. Matrix string theory is related to M(atrix) theory in the same sense that superstring theory is related to M-theory.
M(atrix) theory is written in terms of interacting zero-dimensional Dirichlet branes in infinite momentum frame. It was proposed by Banks, Fischler, Shenker, and Susskind in 1996. See also the discussion in M-theory.
- L. Motl, "Proposals on nonperturbative superstring interactions". arXiv:hep-th/9701025.
- R. Dijkgraaf, E. Verlinde, H. Verlinde, "Matrix String Theory", Nucl. Phys. B 500, p 43 (1997)arXiv:hep-th/9703030.
- N. Ishibashi, H. Kawai, Y.Kitazawa, A. Tsuchiya, "A large-N reduced model as superstring", Nucl. Phys. B 498 (19970 467 arXiv:hep-th/9612115.
- T. Banks, W. Fischler, S.H. Shenker and L. Susskind, "M Theory As A Matrix Model: A Conjecture". Phys. Rev. D55 (1997). arXiv:hep-th/9610043.
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