(8a) Lewis remained an obstinate man.
In this case, the NP to the right of the verb does not identify an object that is separate from the subject, as was the case with transitive verbs. Effectively, this NP renames the subject. If we think about what's going on here in terms of predication, the second NP predicates something (that is, it makes an assertion) about the subject. Contrast that with transitive sentences like (4) above, repeated here for convenience:
(4) Bob kicked John.
Here, the second NP (Bob) doesn't predicate anything about the subject (John) directly. Only the entire verb phrase does the predication. For this reason, these phrases are not called objects but subject complements, because they complete (complement) the meaning of the subject.
Because the NP after the verb is not a distinct object, linking verbs are not transitive. They are a special kind of intransitive verb, one with complex predication. One consequence of being intransitive verbs is that linking verbs cannot be made passive:
(8a) *An obstinate man was remained by Lewis.
Linking verbs can also be followed by an adjective phrase, in which case the AdjP describes some characteristic of the subject:
(9) The president looked haggard.
Whether this phrase is an AdjP or an NP, it fills the same grammatical role: subject complement.
Linking verbs are a small class. Some examples: seem, become, remain, taste, smell, feel. We will label such verbs VL.
The most common verb in English, and also the most irregular, is to be. This verb is generally considered a linking verb. Like other linking verbs, BE can take a subject complement, either an NP or an AdjP:
(10) That toddler is a hyperactive child. [NP: subject complement]
(11) Dorothy Parker was witty. [AP: subject complement]
Unlike other linking verbs, you can also follow BE with a modifier that indicates a place, either literally or metaphorically:
(12a) My mother was in the next room. [PP: place]
Ordinary linking verbs do not permit this construction:
(12b) *My mother became in the next room.
We will label BE as another linking verb, but you should be aware of its differences from other members of this category. Later we will find still more ways in which BE is an exceptional verb.
 Many grammar books treat linking verbs as a separate category, neither transitive nor intransitive, but we are considering transitivity to be a binary quality. Any verb can be categorized as transitive or intransitive, but there is more to verb-phrase structure than just transitivity.
 Some grammar books call subject complements either predicate noun or predicate adjective depending on whether they are noun phrases or adjective phrases, but we will not use those terms, because they blur the distinction between form (NP or AdjP) and function (subject complement).
 By writing the verb in capital letters, we mean any of the forms of the verb. In this instance, BE includes am, are, is, was, were, be, been, and being.