CHAPTER Algebraic identification of under-determined mixtures P. Comon and L. De Lathauwer As in the previous chapters, we consider the linear statistical model below x = As + b 9 (9.1) where x denotes the P -dimensional vector of observations, s the N -dimensional source vector, A the P × N mixing matrix and b an additive noise, which stands for background noise as well as modeling errors. Matrix A is unknown deterministic, whereas s and b are random and also unobserved. All quantities involved are assumed to take their values in the real or complex field. It is assumed that components s n of vector s are statistically mutually independent, and that random vectors b and s are statistically independent. The particularity of this chapter is that the number of sources, N , is assumed to be strictly larger than the number of sensors, . Even if the mixing matrix were known, it