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


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

