🚀 go-pugleaf

Hi all,

I'm doing a least mean square identification of a system. Let's say I
have a group of vectors X (1024 rows by 2 columns) and another one Y
(1024x3). I want to find the matrix A (2x3) the L2 norm of each column
of:
Y - XA

It's a classical problem and we solve the system (apostrophe meaning
transpose):
X'(Y-XA) = 0
A = inv(X'X) X' Y

Now, I want to reverse the problem. Instead of trying to best predict Y
with X, I want to best predict X with Y. The matrix B (3x2) must
minimize the L2 norm of each column of:
X - YB

And the solution is
B = inv(Y'Y) Y' X

So far, so good. But here's my question. Can we predict the zeros in A
from the zeros in B:
B(i,j) = 0 <=> A(j,i) = 0

I have some counter example, but if we create X as a linear transform
from Y, then I cannot find counter examples anymore. Also, it is in the
context of data analysis, so I do a t-test to decide whether a
coefficient is zero or not.

Any pointer would be appreciated!

Thanks,
Tony