General Term: Algorithms. The broad problem of matrix algebra is taken up from the perspective of functional program-ming. Akey question is how arrays should be represented in order to admit good implementations of well-known e cient algorithms, and whether functional architecture sheds any new light on these or other solutions. It relates directly to disarming the \aggregate update " problem. The major thesis is that 2 d-ary trees should be used to represent d-dimensional arrays � ex-amples are matrix operations (d = 2), and a particularly interesting vector (d = 1) algorithm. Sparse and dense matrices are represented homogeneously, but at some overhead that appears tolerable � encouraging results are reviewed and extended. A Pivot Step algorithm is described which o ers optimal stability at no extra cost for searching. The new results include proposed sparseness measures for matrices, improved performance of stable matrix inversion through re-peated pivoting while deep within a matrix-tree (extendible to solving linear systems), and a clean matrix derivation of the vector algorithm for the fast Fourier transform. Running code is o ered in the appendices.