Wielandt Deflation is a type of [[Deflation Methods|Deflation Method]] used to reduce the [[Rank]] of a [[Matrix]]. Find an [[Eigenvalue|Eigenvalues]] $\lambda_{1}$ and [[Eigenvector|Eigenvector]] $\vec v_{1}$. Choose $i$ to be the index of a term of $\vec v_{1}$ that is $v_{1,i} \neq{0}$. $\huge \begin{align} \let \vec x &= \frac{1}{\lambda_{1} \vec v_{1,i}} \mat{ a_{i,1} \\ a_{i,2} \\ \vdots \\ a_{i,n} } \end{align}$ $\huge \begin{align} A\vec v_{1} &= \lambda_{1} \vec v_{1} \\ \vec x^{\intercal} \vec v_{1} &= \frac{1}{\lambda_{1} \vec v_{1,i}}\mat{a_{i,{1}} & \cdots & a_{i,n}}\vec v_{1} \\ &= \frac{1}{\lambda_{1}\vec v_{1,i}} \lambda_{1} v_{1,i} \\ &= 1 \end{align} $