Unformatted text preview: inversions, and therefore is even. • 52413 has 4 + 1 + 2 + 0 = 7 inversions, and therefore is odd. Deﬁnition 5. The sign of a permutation is (1) number of inversion in other words, it is +1 if the permutation is even and1 if the permutation is odd. Deﬁnition 6. Let A be a n × n matrix. Then we deﬁne the determinant of A : det A = X permutations j 1 ,...,j n sign · a 1 ,j 1 a 2 ,j 2 ··· a n,j n This deﬁnition may appear confusing, so we will do some examples to see what this formula means in class. This sum is very large (has n ! terms) if n is large, so we will need other ways to compute the determinant, which we will introduce in the next section. The purpose of this formula is to show that there is such a thing as a determinant at all. 1...
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 Spring '08
 Bens
 Linear Algebra, Algebra, Determinant, Group Theory, Permutations, Bijection

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