Given 2 lattices: $\Lambda_A$ and $\Lambda_B$, where A and B - the basis matrices of the equal dimension. How to check if these lattices are isomorphic?
As I understand, it's enough to show that A can be derived from B using translation, scaling and rotation, but how do I do that? Or is there a better way?
Thank you.
Showing that $A$ can be derived from $B$ using translation, scaling, and rotation is the same as showing that there exists is a matrix $M$ such that $A$ = $M^tBM$. You can do this brute-force, just checking matrices until you find one that works; more systematically and practically (by hand), write $A$ and $B$ as an augmented matrix and row reduce until $A$ is the identity matrix; then $M$ will be the $B$ side of the (reduced) augmented matrix.