Direct sums of bilinear algorithms

We consider the bilinear complexity of certain sets of bilinear forms. We study a class of direct sums of bilinear forms. For this class of problems we show that the bilinear complexity of one direct sum is the sum of the bilinear complexities of the summands and that every minimal bilinear algorithm for computing the direct sums is a direct-sum algorithm. We also exhibit some sets of bilinear forms which belong to this class. © 1981.