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'''THE DETERMINANT''' | '''THE DETERMINANT''' | ||
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| + | == Definition== | ||
Definition: Let A = <nowiki>[aij]</nowiki> be an n x n matrix. The '''determinant''' function, denoted by '''det''', is defined by | Definition: Let A = <nowiki>[aij]</nowiki> be an n x n matrix. The '''determinant''' function, denoted by '''det''', is defined by | ||
| − | det(A) = <math>sum((a1j1)(a2j2)...(anjn))</math> | + | det(A) = <math>sum\{((a1j1)(a2j2)...(anjn))}</math> |
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. | 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. | ||
[[Category:MA265Fall2012Alvarado]] | [[Category:MA265Fall2012Alvarado]] | ||
Revision as of 11:40, 8 December 2012
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.
