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'''THE DETERMINANT'''
 
'''THE DETERMINANT'''
  
----
+
 
 +
== 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 12:40, 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.

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