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December 10th, 2016, 08:21 PM   #1
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Gram-Schmidt

Suppose that $\displaystyle \mathbb{R}^2$ has the inner product defined by the equation $\displaystyle <\vec{u} ,\vec{v} > = \vec{u}^T A^T A\vec{v}=(A\vec{u}) \cdot (A\vec{v})$, being $\displaystyle A = \begin{bmatrix}
2 & -3\\
0& 2
\end{bmatrix}$. Be $\displaystyle B = { \vec{i}, \vec{j} }$ the canonical basis of $\displaystyle \mathbb{R}^2$. Using the Gram-Schmidt process in the vectors of $\displaystyle B$, Find an orthonormal basis for $\displaystyle \mathbb{R}^2$. Use $\displaystyle \vec{i} = \begin{bmatrix}
1\\
0
\end{bmatrix}$ and $\displaystyle \vec{j} = \begin{bmatrix}
0\\
1
\end{bmatrix}$ .
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