Decomposição de Matrizes Antiautossimilares em Matrizes de Posto-1 e Aplicações em Processamento de Sinais

This work defines a new kind of matrix symmetry, through the concept of anti-self-similar matrices. A method of expanding an arbitrary anti-self-similar matrix as a linear combination of rank-one matrices is presented. As an illustration of the proposed techniques, fast algorithms for computing quaternion and octonion multiplications are shown.