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My guess is, it only holds one way i.e. $A>B$ then $\sqrt{A}>\sqrt{B}$ but not otherwise. Any proof or counterexample would be appreciated.

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marked as duplicate by user1551, dfeuer, Dennis Gulko, mau, martini Oct 16 '13 at 8:08

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  • $\begingroup$ Does A > B means , all the element of Mat A > all the element of Mat B ?? $\endgroup$ – Shravan40 Oct 16 '13 at 4:55
  • $\begingroup$ $A>B$ refer to partial ordering of SPD matrices. It implies $A-B$ is positive definite $\endgroup$ – piyush_sao Oct 16 '13 at 4:56
  • $\begingroup$ Your guess is true. $\endgroup$ – user1551 Oct 16 '13 at 6:22