Adaptive filters for broadband beainforming are two-dimensional filters with one dimension being space and the other dimension being time. The filtering in the time dimension is a simple convolution, hence fast algorithms can exploit computational redundancy in this dimension. The filtering in the space dimension is an arbitrary linear combiner, and for reasons arising from various implementation considerations, it is desirable to use factorized estimation techniques in this dimension. In this paper, we present scalar implementations of multichannel fast Recursive Least-Squares algorithms in transversal filter form (so-called FTF algorithms). The point is that by processing the different channels sequentially, i.e. one at a time, the processing of any channel reduces to that of the single-channel algorithm. This sequential processing decomposes the multichannel algorithm into a set of intertwined single-channel algorithms. Geometrically, this corresponds to a modified Gram-Schmidt orthogonalization of multichannel error vectors. Algebraically, this technique corresponds to matrix triangularization of multichannel error covariance matrices and converts matrix operations into a regular set of scalar operations. Algorithm structures that are amenable to VLSI implementation on arrays of parallel processors naturally follow from our approach. Numerically, the resulting algorithm benefits from the advantages of triangularization techniques in block-processing, which are a well-known part of Kalman filtering expertise. Furthermore, recently introduced stabilization techniques for proper control of the propagation of numerical errors in the update recursions are also incorporated.