figuring out orthonormal basis for a matrix?











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For $T in mathcal{L}(mathbb{R}^2)$ given by $T(x,y) = (x, -y)$, its basis is $ mathcal{M}(T) = begin{pmatrix}1 & 0\0 & -1end{pmatrix}$. How would I find the orthonormal basis for this? Is $frac{1}{sqrt{2}}(x + y), frac{1}{sqrt{2}}(x - y)$ one? How would I figure this out?










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  • It is the usual basis ${(1,0), (0,1)}$.
    – Kavi Rama Murthy
    2 days ago















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For $T in mathcal{L}(mathbb{R}^2)$ given by $T(x,y) = (x, -y)$, its basis is $ mathcal{M}(T) = begin{pmatrix}1 & 0\0 & -1end{pmatrix}$. How would I find the orthonormal basis for this? Is $frac{1}{sqrt{2}}(x + y), frac{1}{sqrt{2}}(x - y)$ one? How would I figure this out?










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  • It is the usual basis ${(1,0), (0,1)}$.
    – Kavi Rama Murthy
    2 days ago













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up vote
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down vote

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For $T in mathcal{L}(mathbb{R}^2)$ given by $T(x,y) = (x, -y)$, its basis is $ mathcal{M}(T) = begin{pmatrix}1 & 0\0 & -1end{pmatrix}$. How would I find the orthonormal basis for this? Is $frac{1}{sqrt{2}}(x + y), frac{1}{sqrt{2}}(x - y)$ one? How would I figure this out?










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user589759 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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For $T in mathcal{L}(mathbb{R}^2)$ given by $T(x,y) = (x, -y)$, its basis is $ mathcal{M}(T) = begin{pmatrix}1 & 0\0 & -1end{pmatrix}$. How would I find the orthonormal basis for this? Is $frac{1}{sqrt{2}}(x + y), frac{1}{sqrt{2}}(x - y)$ one? How would I figure this out?







linear-algebra






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  • It is the usual basis ${(1,0), (0,1)}$.
    – Kavi Rama Murthy
    2 days ago


















  • It is the usual basis ${(1,0), (0,1)}$.
    – Kavi Rama Murthy
    2 days ago
















It is the usual basis ${(1,0), (0,1)}$.
– Kavi Rama Murthy
2 days ago




It is the usual basis ${(1,0), (0,1)}$.
– Kavi Rama Murthy
2 days ago















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