Is there a name for the following type of matrix (probably not) , or (more possibly) some context or application where they appear?
(1) each entry is 1, 0, or -1 (2) the entries in each row add to 1 (3) each column vector only occurs once, and no column and its negative both appear. (4) the zero vector is not allowed as a column
For example, if there are two rows the matrices 1 -1 0 1 0 -1 and 1 -1 0 -1 0 1 satisfy the conditions. For n rows I believe the maximum number of columns is 3^(n-1) and there is a simple recursive procedure to generate a matix of this size that satisfies the conditions.