I am not familiar with this topic and have a naive question about QZ decomposition, which is defined as
For any matrix A and B in $\mathbb{R}^{n\times n}$, there exists orthogonal Q and Z, s.t. $QAZ=T$ upper-quasi triangular and $QBZ=S$ upper triangular.
My question is, could this mapping from $(A,B)$ to $(Q,QA,QB)$ unique (with some ordering and normalization)? Then is it continuous?
Any form of help would be appreciated, thank you so much!