de·ter·mi·nant / diˈtərminənt/ • n. 1. a factor that decisively affects the nature or outcome of something: pure force of will was the main determinant of his success. ∎  Biol. a gene or other factor that determines the character and development of a cell or group of cells in an organism, a set of which forms an individual's idiotype.2. Math. a quantity obtained by the addition of products of the elements of a square matrix according to a given rule.• adj. serving to determine or decide something.

determinant A number associated with a square matrix of numbers. The determinant of an n×n matrix A is denoted by det(A) or |A| and given by

where the sum is taken over all n! permutations σ = σ₁σ₂…σ_n

of the integers 1,2,…,n. par(σ), the parity of σ, is either +1 or –1 depending on whether σ is an even permutation or an odd permutation.