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THE DETERMINANT


Definition

Definition: Let A = [aij] be an n x n matrix. The determinant function, denoted by det, is defined by

det(A) = $ \sum{((a1j1)(a2j2)...(anjn))} $

where the summation is over all permutations j1, j2... jn of the set S = {1, 2, ..., n}. The sign is taken as + or - according to whether the permutation j1, j2, ... jn is even or odd.

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