Mr.smith has received a letter (which is)inviting to give a lecture in Princeton Institute.
里面可以看作是个定语从句省略了which is,因为信件里面内容说是邀请去演讲.谢谢大家的帮忙。 还有点小问题想请教一下:我想问的是如果I have received a letter( to invite you to give a lecture ). 括号中的内容可以当作a letter 来讲吗? 还是作目的状语呢?