# Definitions for: Determinant

[n] a determining or causal element or factor; "education is an important determinant of one's outlook on life"
[n] a square matrix used to solve simultaneous equations
[adj] having the power or quality of deciding; "the crucial experiment"; "cast the deciding vote"; "the determinative (or determinant) battle"

Webster (1913) Definition: De*ter"mi*nant, a. [L. determinans, p. pr. of
determinare: cf. F. d['e]terminant.]
Serving to determine or limit; determinative.

De*ter"mi*nant, 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;

Note: 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.

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.

Synonyms: causal factor, crucial, deciding(a), decisive, determinative, determinative, determiner, determining factor, determining(a)