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Antennas with identical radiation patterns can differ in the manner and extent to which they modify an incident wave, i.e., in the way they scatter. This paper enlarges on the work of Dicke  on this subject, employing, as he does, a scattering representation based on spherical modes. However, the approach is more physical and includes antennas with nonreciprocal components and with (local) ports. A canonical minimum-scattering antenna is defined as one which becomes "invisible" when the accessible waveguide terminals are open-circuited. The scattering matrix of such an antenna is shown to be unique once arbitrary orthogonal radiation patterns have been specified. Neither an impedance nor an admittance matrix for such an antenna exists. It is demonstrated for a large class of antennas terminated by matched receivers that the scattered power is generally greater than the absorbed power, equality being attained for minimum-scattering antennas.