QM Sankar 2nd edition -- gram schmidt process on example 1.3.2

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SUMMARY

The discussion focuses on the Gram-Schmidt process as applied to example 1.3.2 from QM Sankar's 2nd edition textbook. The user attempts to compute the orthogonalization of vectors u1=(3,0,0), u2=(0,1,2), and u3=(0,2,5) but encounters issues with the inner product calculation yielding zero. The conversation emphasizes the importance of understanding the underlying theorem and maintaining consistent notation throughout the process. The user expresses a clearer understanding after further study and is now able to proceed with the problem.

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bugatti79
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Hi

I was trying the gram schmidt process on example 1.3.2 page 43 as shown below
u1=(3,0,0), u2=(0,1,2), u3=(0,2,5)v1=u1=(3,0,0)
v2=u2-proj_(w1) u2=(0,1,2)-((<0,1,2><3,0,0>)/9)(3,0,0)

However the top line inner product gives 0...
 
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Lets try to walk you through this.
First do you know what you are actually doing? i.e. explain the gram-schmidt process in a few lines

Second, have you understood the theorem? What does it tell you? (bonus: why do we need it)

And finally why have you used different notation?
I wouldn't advise changing notation before you are certain you really get what is happening.
 
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I have been studying this further. It is clearer to me now and I now know how to proceed with this problem. Thanks
 

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