gram-schmidt process

definition

• a process use when wanting to make an orthonormal basis from any set (1) of linear indep vectors, but (2) not containing already-orthogonal vectors

process

• having set of vectors $u$ and $v$

1. set $u_1$ = $v_1$
2. we have ${\vec{u}}_k={\vec{v}}_k-{\sum }_{i=1}^{k-1}{\frac{<\overrightarrow{v_k},\overrightarrow{u_i}>}{|\overrightarrow{u_i}{|}^2}\vec{u}}_i$
3. normalize: $e_k=\frac{u_k}{||u_k||}$

• illustration
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