Substitute A = SAS-1 into the product (A - )"1 I) (A - A2I) (A - AnI) and explain why
Chapter 6, Problem 32(choose chapter or problem)
Substitute A = SAS-1 into the product (A - )"1 I) (A - A2I) (A - AnI) and explain why this produces the zero matrix. We are substituting the matrix A for the number A in the polynomial peA) = det(A - AI). The Cayley-Hamilton Theorem says that this product is always peA) = zero matrix, even if A is not diagonalizable.
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