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:# Let <math>v_1 \in \mathbb{C}^n</math> be an arbitrary vector with norm <math>1</math>.
:# Abbreviated initial iteration step:
:## Let <math> w_1' = A v_1 </math>.
:## Let <math> \alpha_1 = w_1'^* v_j </math>.
:## Let <math> w_1 = w_1' - \alpha_1 v_1 </math>.
:# For <math> j=2,\dots,m </math> do:
:## Let <math> \beta_j = \left\| w_{j-1} \right\| </math>.
:## If <math> \beta_j \neq 0 </math> then let <math> v_j = w_{j-1} / \beta_j </math>,
:##: else pick as <math>v_j</math> an arbitrary vector with norm <math>1</math> that is orthogonal to all of <math> v_1,\dots,v_{j-1} </math>.
:## Let <math> w_j' = A v_j </math>.
:## Let <math> \alpha_j = w_j'^* v_j </math>.
:## Let <math> w_j = w_j' - \alpha_j v_j - \beta_j v_{j-1}
:# Let <math>V</math> be the matrix with columns <math> v_1,\dots,v_m </math>. Let <math>T = \begin{pmatrix}
\alpha_1 & \beta_2 & & & & 0 \\
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\end{pmatrix}</math>.
Hmm… Better check that the orthogonalisation is stated correctly even for complex elements. [[Special:Contributions/130.243.68.122|130.243.68.122]] ([[User talk:130.243.68.122|talk]]) 15:
== Define variables ==
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