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Linear Algebra : Diagonalizing Matrices

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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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 ...

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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.