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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.

Alumni Liaison

Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale.

Dr. Paul Garrett