# Is such a matrix possible?

1. Mar 3, 2013

### bb700092

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. $\sum$j wij = 1 for all i.
2. Sum of squares of all elements of each column is equal to one, i.e. $\sum$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.

2. Mar 3, 2013

### AlephZero

The simplest counter example is when k = 1 and n > 1.