Linking verbs are a sub-group of stative verbs that denote a state of being, connecting the subject with a complement, usually an adjective describing the subject (not the verb). Dynamic verbs, by contrast, are followed by adverbs modifying them, rather than by adjectives.
Linking Verbs with Typical Adjectives Following Them
State of Being Senses Transformation
keep (quiet) look (young)
feel (tired) become (suspicious)
His new girlfriend looks really good.
[looks (Present Simple form of look) as linking verb meaning to have the appearance of, as a state]
He has been frantically looking for his glasses all morning.
[has been looking (Present Perfect Progressive form of look) as dynamic verb meaning to search for something, as an action]