What does "determinant" mean?

Additional senses

1. 2.(Math.) The sum of a series of products of several numbers, these products being formed according to certain specified laws; thus, the determinant of the nine numbers. a, b, c,a', b', c',a'\'b7, b'\'b7, c'\'b7, is a b' c'\'b7 -- a b'\'b7 c' + a' b'\'b7 c] -- a' b c'\'b7 + a'\'b7 b' c. The determinant is written by placing the numbers from which it is formed in a square between two vertical lines. The theory of determinants forms a very important branch of modern mathematics.
2. 3.(Logic) A mark or attribute, attached to the subject or predicate, narrowing the extent of both, but rendering them more definite and precise. Abp. Thomson.