I came across this package via a PkgEval run in JuliaLang/julia#46874. I found that currently GivensQ subtypes Factorization, but is actually meant to represent an orthogonal/unitary matrix. So you may want to consider to subtype LinearAlgebra.AbstractQ. After JuliaLang/julia#46196, you could "benefit" from a lot of generic fallbacks that do exactly what you want it to do. You can check the generic part, the beginning of the new file abstractq.jl in that PR, and the added test there to see how it feels and works.