Linear independence of steering vectors of an electromagnetic vector sensor

We investigate linear independence of steering vectors of one electromagnetic vector sensor. We show that every three steering vectors with distinct directions of arrival (DOAs) are linearly independent. We also show that four steering vectors with distinct DOAs are linearly independent if the ellipticity angles of the signals associated with any two of the four steering vectors are distinct. Moreover, every four steering vectors corresponding to circularly polarized signals with the same spin direction are linearly dependent. We then establish that five steering vectors are linearly independent if exactly two or three of them correspond to circularly polarized signals with the same spin direction. Finally, we demonstrate that given any five steering vectors, then for any DOA there exists a steering vector that is linearly dependent on the five steering vectors.