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Question: Let's say you wanted to perform a sequence of N transforms T_1, T_2, T_3,...T_N on 1 million points. Would you perform N-million matrix-vector multiplications, or is there a more efficient way to perform the computation?


No, one can just perform N matrix multiplications to compose T_1, T_2.. T_N and then multiply that single T_compose with 1 million points. Hence in total there will be N + million matrix multiplications.