Question

Let $\mathbf{A}$ be a diagonalizable matrix. Prove that $\mathbf{A}^T$ is diagonalizable.

   Let $\mathbf{A}$ be a diagonalizable matrix. Prove that $\mathbf{A}^T$ is diagonalizable.

Elementary Linear Algebra

Elementary Linear Algebra

Stephen Andrilli,… 5th Edition

Chapter 3, Problem 18

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A matrix $\mathbf{A}$ is said to be diagonalizable if there exists an invertible matrix $\mathbf{P}$ and a diagonal matrix $\mathbf{D}$ such that $\mathbf{A} = \mathbf{P} \mathbf{D} \mathbf{P}^{-1}$. Show more…

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Let $\mathbf{A}$ be a diagonalizable matrix. Prove that $\mathbf{A}^T$ is diagonalizable.

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