Question

How do you solve for this matrix.
X*X^t=0?

What matrix times its tranpose is zero?

If we use the usual notation:

A_{i,j} for the element at the i-th row and j-th column then, if we put:

A = X X^(T) ---->

A_{i,j} = X_{i,k}[X^(T)]_{k,j} =

X_{i,k}X_{j,k}

here we sum over the repeated index k.

The A_{i,j} have to b zero for all i and j. The term

X_{i,k}X_{j,k}


is an inner product of the i-th and j-th row of the matrix X. So, you have to fill the rows such that all the inner products are zero. That's easy to do.
E.g. take the first row as:

[1,i,0,0,0,0...] and fill all other rows with zeroes. The inner product of the first row with itself is then zero and inner products involving other rows are then also zero.

Thanks for your help. If your good you can also try to answer my other optimization problem:)