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nominative absolute

n. (context grammar English) A grammatically independent element of a sentence realized in English as a noun phrase and a participle or adjective.

Wikipedia
Nominative absolute

In English grammar, a nominative absolute is a free-standing ( absolute) part of a sentence that describes the main subject and verb. It is usually at the beginning or end of the sentence, although it can also appear in the middle. Its parallel is the ablative absolute in Latin or the genitive absolute in Greek.

One way to identify a nominative absolute is to add a conjunction and a verb: one can always create a subordinate clause out of a nominative absolute by adding a subordinate conjunction (such as "after" or "because") and a form of the verb to be.

Examples The dragon slain, the knight took his rest. The battle over, the soldiers trudged back to the camp.

In each case, if a conjunction such as "after" or "because" were added before the nominative absolute as well as the verb "was", the absolute would become a subordinate clause.

Because the dragon was slain, the knight took his rest. After the battle was over, the soldiers trudged back to the camp.