The additive complexity of a nondegenerate matrix of size n is the minimum number of additions in a chain of elementary transformations over rows required to reduce the matrix to the identity one. It is shown that if ...
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The additive complexity of a nondegenerate matrix of size n is the minimum number of additions in a chain of elementary transformations over rows required to reduce the matrix to the identity one. It is shown that if the order of the field tends to infinity, then almost all matrices are of maximum possible additive complexity ( n - 1) n. The matrices of additive complexity ( n - 1) n are shown to be M D S-matrices.
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