(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

First off, this isn't for a class, I'm just going over some material, however this does come from a textbook, so I figure this is a reasonable place to ask the question! Here's the question:

Use the Gram-Schmidt procedure to orthogonalize the following vectors:

v1=[(1+i),1,i]

v2=[i,3,1]

v3=[0,28,0]

2. Relevant equations

Let's not even worry about v3 right now. Let's just orthogonalize v1 and v2.

3. The attempt at a solution

First off, we let v1=u1 = [(1+i),1,i]

Now, we can find u2 by: [tex]u2 = v2 - \frac{<u1,v2>}{||u1||^2}u1[/tex]

The norm of u1 is 2, therefore squaring that we get 4.

When I took <u1,v2> I got 4. Therefore 4/4 = 1.

This leaves us with u2 = v2 - u1 = (-1,2,1-i)

HOWEVER, u2 dot u1 = 2

and of course if they were orthogonal they should equal 0.

Not sure where I made a mistake... so if anyone can help that would be appreciated!

cheers,

-astropi

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# Gram-Schmidt Question

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