Theorem 2.3 here says that if $A$ is normal it has a positive semi-definite square root.

Isn't this wrong? In particular the fourth sentence of the proof claims the eigenvalues of normal matrices are positive, which seems way off...

  • $\begingroup$ You're correct. That theorem is nonsense. Any diagonal real matrix with some negative entry is a counterexample. $\endgroup$ – Ted Shifrin Sep 22 '16 at 7:34
  • $\begingroup$ Apparently "normal" is a typo for "positive semi-definite". $\endgroup$ – Robert Israel Sep 22 '16 at 7:43

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