You are not logged in.
Pages: 1
Let G = {M1, M2, ... , Mr} denote the set of n × n permutation matrices (those matrices which have only zeroes and ones as entries, and whose row and column sums are all one), and let A = (M1 + M2 + ... + Mr) / r denote the average of these matrices. Determine A.
Offline
There are n! total matrices in the set G. The total sum of every element in a given matrix is n, which means that the total sum of every element in all of the matrices in G is n * n!. Dividing by n!, the total number of matrices in G, we find that the total sum of every element in A is n. Every element will have the same value, so this means that A is an nXn matrix where every element has the value 1/n.
Wrap it in bacon
Offline
Pages: 1