It is said that the omission of "to be" is allowed only when the adjective (phrases), noun (phrases), or prepositional phrase comes after the to be like this:
a He seemed (to be) angry about the decision.
b This seemed (to be) of great importance.
c She seemed (to be) a great player.
But I found some strange things about it. For example, this.
d He seemed excited by the news.
Well, excited by the news is definitely not an adjective phrase. Were the to be inserted in it, it would describe the action like this: the news excited him. So "excited" would be a past participle used as a verb after an auxiliary verb, not an adjective.
Like in a passive voice where the participles after the "to be" are considered verbal, or stative, participle phrase when not considered a pure adjective.
e He was bored by the music. <- bored by the music is not an adjective phrase but a stative, or verbal, participle phrase.
So why is it possible to say sentence d when "excited by the news" is a stative phrase not an adjective phrase? Wouldn't it be equivalent to deleting to be with present participle like this : He seemed doing the job.
Edit: What I referred to as stative past participle is known as dynamic passive by many. I think Wikipedia had some problem. http://www.grammarphobia.com/blog/2008/11/stative-seeking.html