Siberian Federal University

The paper considers the matrix ball in the space of rectangular matrices and studies the group of holomorphic automorphisms: explicit formulas are obtained for fractional-linear transformations preserving the ball, and their general structure is proved. Special attention is paid to the construction of an automorphism mapping a given interior point of the ball to the origin. The results generalize the classical theory of automorphisms of the unit ball in Cn and the ball of square matrices to the case of rectangular matrices