Similarity of Matrix
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Mathematics/Linear Algebra
Similar Definition 1. Let A,B∈Mn×n(F). We say that B is similar to A if ∃Q∈Mn×n such that Q is invertible and B=Q−1AQ. Property Property. Let A,B∈Mn×n(F) be the similar matrices. Then (a) A and B have the same characteristic polynomial. Proof. (a) Since A and B are similar, ∃ invertible $Q \in M_{n \times n}(F)..