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    Linear Algebra : Diagonalizing Matrices

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    Let B be an nxn matrix with B^2 = B prove that B is diagonalizable, ie there exists an invertible matrix S so that S^-1 B S is diagonal. (Hint: all eigenvalues of B are either 0 or 1. For each k between 0 and n, consider the case when the nullity of B is k.)

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    Solution Preview

    Here we must consider some facts first and then get the answer step by step:

    The minimal polynomial of a matrix A is the unique basis for the ideal of polynomials such that the matrix A vanishes on them.

    According to the Cayley-Hamilton theorem if ...

    Solution Summary

    Matrix diagonalization is investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who posted the question.