My Last Duchess poem's critical appreciation?

The poem "My Last Duchess" is about a duke who loves his wife too much. He also feels jealous that she treats everybody with the same attitude--her servants or husband or anyone else. She gave them all the same smile, when someone gave her a flower or her husband gave her a precious gift. All are equal in her eyes.

One day her husband became fed up with this kind of attitude and killed her. And on the other day, he called a famous painter who made his wife's beautiful portrait.