Question
The argument earlier in this chapter shows that, if $A$ is Hermitian and $\|A(h)\| \leq b\|h\|$ for all $h$, with $b<0$, then $A$ is invertible. Find an example to show that the requirement that $A$ be Hermitian is actually necessary.
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Give a reason if true or a counterexample if false: (a) If $A$ is Hermitian, then $A+i l$ is invertible. (b) If $Q$ is orthogonal, then $Q+\frac{1}{2} I$ is invertible. (c) If $A$ is real, then $A+i l$ is invertible.
Eigenvalues And Eigenvectors
Complex Matrices
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