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evinda

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Let $A$ be a $n \times n$ complex unitary matrix. I want to show that the eigenvalues $\lambda$ of the matrix $A+A^{\star}$ are real numbers that satisfy the relation $-2 \leq \lambda \leq 2$.

I have looked up the definitions and I read that a unitary matrix is a square matrix for which $AA^{+}=I$.

(The transpose matrix of $A^{\star}$ is symbolized with $A^{+}$.)

($A^{\star}$: complex conjugate)In order to show that the eigenvalues $\lambda$ of the matrix $A+A^{\star}$ are real numbers and satisfy that $-2 \leq \lambda \leq 2$, do we maybe have to find the minimal polynomial of the matrix $A+A^{\star}$ ? If so, how? Is there a relation? Or do we have to do it somehow else? (Thinking)