determinant has 8 distinct synonyms spread across 3 of its 4 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
a determining or causal element or factor
“education is an important determinant of one's outlook on life”
the site on the surface of an antigen molecule to which an antibody attaches itself
a square matrix used to solve simultaneous equations
having the power or quality of deciding
“the crucial experiment”
Synonyms, antonyms and the broader and narrower relations for determinant come from Princeton University’s WordNet. Full sources and licences.