ABSTRACT
Let M be an n × n matrix with real entries. Two fundamental quantities associated with an n×n matrices are the determinant and permanent, whose definition we recall below.
det(M) = ∑ σ∈S n
perm(M) = ∑ σ∈S n
Here S n is the group of permutations of the set [n] = {1, 2, . . . , n}. For σ ∈ S n, sgn(σ) is its signature - this is 1 if the set {(i, j)|1 ≤ i < j ≤ n, σ(i) > σ( j)} has even cardinality and it is −1 otherwise.
