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Proof : Diagonalization of Matrices

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Write a proof for the following statement:
If A is an n x n upper triangular matrix with no two diagonal elements the same, then A is similar to a diagonal matrix. Show work.

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The similarity to a diagonal matrix is investigated.

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1. Write a proof for the following statement:
If A is an n x n upper triangular matrix with no two diagonal elements the same, then A is similar to a diagonal ...

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