Category:Gram-Schmidt Orthogonalization

This category contains pages concerning Gram-Schmidt Orthogonalization:

Let $\struct {V, \innerprod \cdot \cdot}$ be an inner product space over $\R$ or $\C$.

Let $S = \set {v_n: n \in \N_{>0} }$ be a linearly independent subset of $V$.

Then there exists an orthonormal subset $E = \set {e_n: n \in \N_{>0} }$ of $V$ such that:

$\forall k \in \N: \span \set {v_1 , \ldots , v_k} = \span \set {e_1 , \ldots ,e_k}$

where $\span$ denotes linear span.

Source of Name

This entry was named for Jørgen Pedersen Gram and Erhard Schmidt.