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I have the following question to answer, but what I would like is a sane and easy to grasp idea of what Normalization is all about(the why, when etc) and then how to do it without it getting over one's head please.

  1. Find an orthonormal basis of $\mathbb{R}^2$ by applying the Gram-Schmidt orthonormalization method to the vectors: $$(1; 2)^T, (2; 1)^T$$

  2. Find a unit vector which is orthogonal to all vectors in the subspace of ${\bf R}^3$ given by: f(x; y; z)T : 3x - 2y + z = 0g

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    Do you mean orthogonalization instead of normalization?2011-07-20
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    I think the description and the attendant picture [at Wikipedia](http://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process#The_Gram.E2.80.93Schmidt_process) are pretty good. Can you use that to do the first problem? I think that if you understand this visually for two vectors, then you are in very good shape.2011-07-20
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    No, I find the wiki explanation a bit too advanced as well. I am in a class to learn this but having a hard time making sense of it.2011-07-20
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    I did a little light editing, but I was stumped by f(x;y;z)T:3x-2y+z=0g. I have no idea what this is supposed to be.2011-07-20

4 Answers 4