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A dynamical fuzzy space might be described by a three-index variableC_{ab}^c, which determines the algebraic relations f_a f_b =C_{ab}^c f_c amongthe functions f_a on the fuzzy space. A fuzzy analogue of the generalcoordinate transformation would be given by the general linear transformationon f_a. I study equations for the three-index variable invariant under thegeneral linear transformation, and show that the solutions can be generallyconstructed from the invariant tensors of Lie groups. As specific examples, Istudy SO(3) symmetric solutions, and discuss the construction of a scalar fieldtheory on a fuzzy two-sphere within this framework.Comment: Typos corrected, 12 pages, 8 figures, LaTeX, JHEP clas

AN INVARIANT APPROACH TO DYNAMICAL FUZZY SPACES WITH A THREE-INDEX VARIABLE