deletions | additions       diff --git a/method.tex b/method.tex  index db3b919..d1fa1f8 100644  --- a/method.tex  +++ b/method.tex 
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$Q'$ is smallest when \[||W^{\frac{1}{2}} \vec{R}(\vec{x} + \vec{\delta x})|| \approx ||W^{\frac{1}{2}}\vec{R}(\vec{x}) + W^{\frac{1}{2}} A\vec{\delta x}||\] is minimized. \par  A matrix $H$ is defined such that $HW^{\frac{1}{2}} A\vec{\delta x}$ is upper triangular. $H$ is orthogonal and can be generated by the product of $m$ Householder operation matrices. Note that the orthogonality of $H$ guarantees that \[|| HW^{\frac{1}{2}}\vec{R}(\vec{x}) + HW^{\frac{1}{2}} A\vec{\delta x} || \\ = ||H(W^{\frac{1}{2}}\vec{R}(\vec{x}) + W^{\frac{1}{2}} A\vec{\delta x})|| \\ = ||W^{\frac{1}{2}}\vec{R}(\vec{x}) + W^{\frac{1}{2}} A\vec{\delta x}||\]   Since $HW^{\frac{1}{2}} A\vec{\delta x}$ is upper triangular, it can be rewritten as   \[ \left( \begin{array} \begin{array}{}  A' \\  0 \\  0 \end{array} \right)\]