CHAPTER Algebraic methods after prewhitening L. De Lathauwer 5 5.1 INTRODUCTION In this chapter we discuss four prewhitening-based algebraic algorithms for Independent Component Analysis (ICA). The prewhitening takes into account the structure of the covariance matrix of the observed data. This is typically done by means of an Eigenvalue Decomposition (EVD) or a Singular Value Decomposition (SVD). The prewhitening only allows one to find the mixing matrix up to an orthogonal or unitary factor. In this chapter, the unknown factor is estimated from the higher-order cumulant tensor of the observed data. This involves orthogonal tensor decompositions that can be interpreted as higher-order generalizations of the EVD.