Hugo Mills on Nostr: Dear #mathstodon Working in N^p, I have two sets of vectors, u_1,...,u_n and ...

Dear #mathstodon

Working in N^p, I have two sets of vectors, u_1,...,u_n and v_1,...,v_m. I'm looking for linear sets of scalars, x_1,....x_n and y_1,...,y_n where

\sum x_i u_i = \sum y_j v_j.

i.e., Ux = Vy (collapsing to a matrix/vector representation).

There's a trivial solution (x_i=y_j=0), but I'm not entirely sure how to find the non-trivial solutions, given that it's all natural numbers.

Any pointers to keywords I can follow up on? A name for the problem?

#math #maths