Questions on Weighted Least Square Estimation This is a page from the book linear algebra,geodesy and gps by Gilbert Strang....
the page explains about the justification of the inverse of the of the co variance matrix of measurement vector $b$ in the over determined system $Ax = b$ as the best weight matrix for best estimate of x.


what does the line errors contained in the matrix mean?(underlined in blue color..)
how does that substitution take place marked with a blue curve...
is E{$rr^T$} = E{$bb^T$} ??


any explanation is welcome...
The linear model is $b=Ax+r$, so you can see the errors $r$ as the noise added to the measurements $b$.
The covariance $\Sigma_b=E\{(b-\bar{b})(b-\bar{b})^T\}=E\{(b-Ax)(b-Ax)^T\}=E\{rr^T\}$
$E\{rr^T\} \neq E\{bb^T\}$ unless $Ax=0$