$A$ is symmetric positive definite matrix and $S$ is such that $A=SS^{T}$. Further 


$y=Sz$  

Does there exist a simple ( or any verifiable) relation exist only involving $A$,$y$ and $z$ ?


Thanks 



Matrix elimination
Your last comment confirms the tentative answer I gave in the comment above. All you need to check is the scalar relation $y^T A^{-1} y = z^T z$.


