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…σn 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.
σ = σ1σ2…σn