Exercise 2.3

Question

Let $A\in \mathbb{C}^{m 	imes m}$ be hermitian. An eigenvector of $A$ is a nonzero vector
$x \in \mathbb{C}^{m 	imes m}$ such that $Ax = \lambda x$ for some $\lambda \in \mathbb{C}$, the corresponding eigenvalue.
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(a) Prove that all eigenvalues of $A$ are real.
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(b) Prove that if $z$ and $y$ are eigenvectors corresponding to distinct eigenvalues, then $x$ and $y$ are orthogonal.

Desh Raj · Accepted Answer

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Exercise 2.3

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Exercise 2.3

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