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RE: Linear Transformations: A 20 SBD coding contest announcement! [EXTENSION UPDATE!]
Your A is a symmetric matrix. So computations for it can be performed much quicker than for (most) non-symmetric matrices.
In addition, if you want to perform linear operation on the arrows that you presented in the input section then the input needs to consist out of pairs where one co-ordinate indicates the arrow starting point and the other co-ordinate indicates the arrow endpoint
That was an example. I agree to your comment. I have done another example here which is not symmetric. By the way we are talking about 2D or 3D cases only. :P