A note on background independence in noncommutative gauge theories, matrixmodel, and tachyon condensation

Using the construction of D-branes with nonzero B field in the matrix model we give a physical interpretation of the known background independence in gauge theories on a noncommutative space. The background independent variab les are identified as the degrees of freedom of the underlying matrix model . This clarifies and extends some recent results about the end point of tac hyon condensation in D-branes with a B field. We also explain the freedom i n the description which is parametrized by a two form Phi from the points o f view of the noncommutative geometry on the worldvolume of the branes, and of the first quantized string theory.