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Given a set of n points and m transformations that are to be applied to each of the points, how can I perform the transformations in < O(nm)?
I tried to understand the solution to this from an article on e-maxx.ru/algo/binary_pow (its English translation), but I was unable to understand the method. Can someone help me out?
From linear algebra we know that a combination of transformations performed sequentially is a transformation itself. Moreover, if all transformations are represented by a matrix, the resulting transformation is represented by a product of our matrices. That's all.
But the best answer for your question will be: just take a book in linear algebra and study it!
Ok!