This is an exercise on the book fundamentals of matrix computations 1st. edition.

It asks to show that for $A \in R^{nxn}$, if $(\lambda, u)$ eigenpair, then $(\overline{\lambda}, \overline{u})$ is also an eigenpair.

  • 3
    $\begingroup$ It helps to note that for $A,B \in \Bbb C^{n \times n}$, we have $\overline{AB} = \bar A \bar B$ (where $\bar A$ denotes the conjugate of $A$). $\endgroup$ – Omnomnomnom Nov 1 '18 at 16:50
  • $\begingroup$ @Omnomnomnom I am sorry, could you give me some more? I am staring at it, but I do not see it still. $\endgroup$ – MTLaurentys Nov 1 '18 at 17:26
  • 1
    $\begingroup$ If $Au = \lambda u$ then $\overline{A} \overline{u} = \overline{A u} = ?$ $\endgroup$ – Connor Harris Nov 1 '18 at 17:49

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