The impedance matrix of an arbitrary multiport array antenna with Ohmic losses was studied. It was assumed that the partial current distributions in the array, corresponding to the alternate exciting one of its terminals while the other ones are open-circuited, are known. Consideration of the power balance in the lossy array antenna has allowed ascertaining that its impedance matrix is a sum of the radiation resistance matrix and loss resistance matrix, which are in general case complex Hermitian matrices and only in some particular cases can be real. The theoretical statements obtained are confirmed by two numerical examples, where analysis of two lossy dipole arrays was performed. In the first example, the dipoles were located above the imperfect ground, which served as a source of losses, and in the second example, the same dipoles were located in free space, and the embedded parasitic element was the source of losses. The results of the analysis showed that the asymmetric placement of energy absorbers in the array antennas leads to the appearance of imaginary parts in the matrices of radiation and loss resistances, which allow one to correctly predict the behavior of the array radiation efficiency during beam scanning.