Is My Solution to the Orthonormalization Process Correct?

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Homework Help Overview

The discussion revolves around the orthonormalization process in linear algebra, specifically focusing on whether the original poster's (OP) solution is correct. Participants are examining the steps involved in normalizing vectors and ensuring they are orthogonal.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the method of normalizing vectors by dividing by their lengths and the subsequent orthogonalization process. The OP questions the correctness of their formula and the placement of vectors in the calculations. Others suggest checking for independence and orthogonality of the vectors.

Discussion Status

The discussion is ongoing, with participants providing guidance on checking the properties of the vectors involved. There is an emphasis on self-verification of the calculations and properties rather than providing direct solutions.

Contextual Notes

There are indications of confusion regarding the terminology used in the orthonormalization process, particularly the distinction between normalizing and dividing by the normal. The OP is also seeking clarification on the correct formula for orthogonalization.

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is that correct??
 
I'm not going to go through all of that calculation! You should be able to check for your self if they are independent (if so then since there are three vectors, yes, they form a basis for the subspace) and if they are orthonormal.

I will make two comments. You do not "divide by the normal". You "normalize" a vector by dividing by its length. And it is generally simpler to normalize each vector (divide by its length) as you calculate each vector, not at the end.
 
Last edited by a moderator:
so first i divide each vector by its length
and then i do the orthogonalization process
did i wrote the orthogonalization formula correctly
??
 
Last edited:
transgalactic said:
so first i divide each vector by its length
and then i do the orthogonalization process
did i wrote the orthogonalization formula correctly
??

After you have found a vector perpendicular to all the previous vectors, divide by its length. That will simplify the rest of the calculation.

Again, check it yourself. Do all the vectors have length 1 (is the dot product of any vector with itself equal to 1)? Are all the vector orthogonal to all the others (is the dot product of two different vectors 0)?
 
ok after,
whats the right formula for the orthogonolazation process

did i used the correct formula??
did i put the vectors in the right place?
 

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