I want a matrix W of size nxk (where n>>k) with the following two properties: 1. Sum of all elements of each row is equal to one, i.e. [itex]\sum[/itex]j wij = 1 for all i. 2. Sum of squares of all elements of each column is equal to one, i.e. [itex]\sum[/itex]i wij2 = 1 for all j. Is such a matrix possible? Any hint at how to prove one way or the other would be appreciated. Thanks in advance.