# Incorrect theorem in preparation for polar decomposition in notes?

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...

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