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 December 10th, 2016, 08:21 PM #1 Newbie   Joined: Dec 2016 From: Natal - Brazil Posts: 10 Thanks: 0 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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