Permanent Biography, Permanent Videos, Permanent Similar artist, Permanent Discography, Permanent Tags
You are in : HOME : P : Permanent :Biography Permanent
In linear algebra, the permanent of a matrix is a function of a matrix
related to the determinant. The permanent as well as the determinant are
polynomials of the entries of the matrix.
Definition The permanent of an n-by-n matrix A = (ai,j) is defined as
operatorname(A)=sum_prod_^n a_.
The sum here extends over all elements σ of the symmetric group Sn,
i.e. over all permutations of the numbers 1, 2, ..., n.
For example,
operatornamebegina&b \ c&dend=ad+bc.
The definition of the permanent of A differs from that of the determinant
of A in that the signatures of the permutations are not taken into account.
If one views the permanent as a map that takes n vectors as arguments, then
it is a multilinear map and i
