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diogotcorreia committed Jul 7, 2024
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Expand Up @@ -221,6 +221,7 @@ Sendo $W$ um espaço euclidiano e $S$ um subespaço de $W$ e $v$ um vetor de $W$
$$
\| x-\op{proj}_Sx\|\le \|x-u\|
$$

para qualquer $u \in S$
:::

Expand Down Expand Up @@ -249,6 +250,7 @@ u_2 &= v_2-\frac{\langle u_1,v_2\rang}{\|u_1\|^2} \\
u_k &= v_k-\op{proj}_{u_1}v_k-\op{proj}_{u_2}v_k-\dots-\op{proj}_{u_{k-1}}v_k
\end{aligned}
$$

é ortogonal.

Os conjuntos U e V geram o mesmo espaço.
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