Given two symmetric positive definite matrices $(A^TA)$ and $(B^TB)$ I need to compute $A^TB$.
$A$ and $B$ are not given directly.
$(A^TA)$ and $(B^TB)$ have the same dimensions. $A$ and $B$ are assumed to have the same dimensions, too.
Is there a way to achieve this?
Have spd $(A^TA)$ and $(B^TB)$, need $A^TB$.
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linear-algebra
matrices
numerical-methods
numerical-linear-algebra
estimation-theory
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2If $M$ is an orthogonal matrix ($M^TM=I$) then $(MA)^TMA=A^TA$ but $(MA)^TB=A^TM^TB\neq A^TB$ in general. Hence you can't determine $A^TB$. – 2012-04-24
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1Could you be bothered to write out whatever "spd" stands for? – 2012-04-24
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0Thanks, user8268. Would you like to make this an answer instead of a comment? – 2012-04-24