The antenna array arrangement determines the rank of the transformation matrix in 1-D mirrored aperture synthesis (1-D MAS). Only when the transformation matrix is of full rank can cosine visibilities be precisely solved from the transformation equations. However, the existing literature states that full rank cannot be realized with the default perpendicular polarization of antennas. In this letter, the transformation matrices of arrays with various polarizations of antennas are discussed, and a type of full array with a full-rank transformation matrix is found. Based on these results, the existence conditions for an array with a full-rank transformation matrix are obtained. In addition, a search algorithm with a shorter search time than the existing algorithm is designed to find low-redundancy arrays with a full-rank transformation matrix. The simulations verify that cosine visibilities are precisely solved from the transformation equations for the array with a full-rank transformation matrix.