  We propose an eigenvector-based formalism for the calibration of radio
interferometer arrays. In the presence of a strong dominant point source, the
complex gains of the array can be obtained by taking the first eigenvector of
the visibility matrix. We use the stable principle component analysis (SPCA)
method to help separate outliers and noise from the calibrator signal to
improve the performance of the method. This method can be applied with poorly
known beam model of the antenna, and is insensitive to outliers or
imperfections in the data, and has low computational complexity. It thus is
particularly suitable for the initial calibration of the array, which can serve
as the initial point for more accurate calibrations. We demonstrate this method
by applying it to the cylinder pathfinder of the Tianlai experiment, which aims
to measure the dark energy equation of state using the baryon acoustic
oscillation (BAO) features in the large scale structure by making intensity
mapping observation of the redshifted 21~cm emission of the neutral hydrogen
(HI). The complex gain of the array elements and the beam profile in the
East-West direction (short axis of the cylinder) are successfully obtained by
applying this method to the transit data of bright radio sources.
