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Determinant

a.
  1. Serving to determine or limit; determinative.

n.
  1. That which serves to determine; that which causes determination.
  2. (Math.) The sum of a series of products of several numbers, these products being formed according to certain specified laws
  3. (Logic) A mark or attribute, attached to the subject or predicate, narrowing the extent of both, but rendering them more definite and precise.

thus, the determinant of the nine numbers a, b, c,a', b', c',a'', b'', c'', is a b' c'' - a b'' c' + a' b'' c] - a' b c'' + a'' 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.