nonsingular matrix (X) in GSVD function

In the description of GSVD function you consider that A = U*C*X', but in the original paper of Van Loan 1976 is A=U*C*X^-1, what is the correct form?

Answer 1

[Christine Tobler]

These are just different but equivalent definitions: Both will result in the same C and S, the only difference is in how X is represented.

The advantage of using X and not its inverse is that this algorithm will also work for cases where X becomes singular, where an inverse could not be taken. This happens if [A; B] does not have full rank.