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## Similar matrices

This isn't specifically Maple-related; but mathematics-related; related to Linear Algebra and Modern Algebra. While reviewing Linear Algebra; I ran across the concept of "Similar Matrices"; which are defined as: if A,B are nxn matrices and there exists invertible nxn matrix P such that P^(-1)*A*P = B then A is similar to B The payoff was: if A, B are similar then they "have the same eigenvalues" (the characteristic equation is same for both A and B). (Here we are talking about the group of invertible nxn matrices, with operation matrix multiplication) -- It was interesting to compare this to conjugate permutations ... who "have the same type". And conjugate elements of a group who "have the same order". (I think that is right, its off the top of my head) So, this conjugacy concept and and conjugate elements having some deep relation is kind of fascinating. Sort of another type of isomorphism. If elements are conjugate, then they are the same in some important way. Some kind of equivalence relation perhaps. -Jay

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