"A lot of people criticised me for working with her and I think so far this week we have shown that women can be very good coaches as well," Murray said after his semi-final victory.
"I’m very thankful to Amelie for doing it and I would say it was a brave choice from her to do it. Hopefully I can repay her for what she did."
"A lot of people were criticising her at the end of last year, like the way I was playing was her fault when I'd spent two weeks training with her up to the end of the year, until the training block. You can't change things during tournaments. There was very little time to spend with each other."
Murray also acknowledged American Madison Keys' recent hiring of Lindsay Davenport, the 19-year-old making her first Grand Slam semifinal here.
"I see no reason why that can't keep moving forward like that in the future," Murray continued. The crowd inside Rod Laver Arena applauded his comments.
"I think it's great," former doubles standout Rennae Stubbs, an Australian TV commentator, wrote in an email to USA Today Sports about Murray's words. "I love the way he is standing behind his decision to work with her."
Stubbs pointed out that Murray's mother has been a constant force in his life. Judy Murray is a respected tennis coach in Britain, and is the current Fed Cup captain there.
"His mother's influence is so obvious," she wrote. "He is such a champion of women
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"It made such big news when Andy picked Amelie, but to me it was like, 'Really? I just don't understand that line of thinking,'" Navratilova said.
"One day people will not look at gender when they hire a coach," Navratilova told The Daily Telegraph. "I saw some comments from Toni Nadal who said that women should not be coaching men because it is a completely different game. But you do not have to be a baseliner to coach another baseliner; it is about what you can bring to that particular player.
"I think you’ll see more women coaches after the results that Amelie has achieved with Andy, because she’s done a really great job. And Lindsay has obviously had quick success with Madison, even if she does have a bazooka of a player to work with. The other thing is that tennis pays better these days, so the money is there to lure the former champions back to the tour.
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"A coach sometimes gets so much praise when their player does well and sometimes gets criticism when they don't do well," said U.S. Fed Cup captain Mary Joe Fernandez, speaking on ESPN2's Australian Open coverage.
Fernandez continued on ESPN2: "I think (Mauresmo is) getting him to be more aggressive. She was a player who loved to come forward – that's how she won her two majors. It's taken a little bit longer with Andy and Mauresmo, but the personalities mesh well. And she's making an impact; she's getting through to him."