How do I find an orthonormal basis for a plane defined as $x_1+x_2+x_3=0$? I don't know where to start -- not even given dimensions. Thank you.
Find an orthonormal basis of a plane
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linear-algebra
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0Do you mean a plane in $\mathbb{R}^3$ given as $ax+by+cz=0$? – 2011-03-04
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1In general: find an arbitrary basis, and apply Gram-Schmidt. – 2011-03-04
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0@Arturo: I am not given dimensions, which is part of my confusion. – 2011-03-04
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0What does "a+b+c=0" mean, then? Are a, b, and c constants? Variables? Do you know the dimension of the ambient space? – 2011-03-04
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0@Arturo: a, b, and c are variables (it was given by x_1 x_2 and x_3 in the textbook). Nothing stated about the dimensions. – 2011-03-04
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1@John: You should stick to $x_1$, $x_2$, and $x_3$. Those are *clearly* variables, whereas $a$, $b$, and $c$ are usually constants or scalars. – 2011-03-04