# Orthonormal procces question

#### transgalactic

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#### transgalactic

is that correct??

#### HallsofIvy

Science Advisor
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.

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#### transgalactic

so first i divide each vector by its length
and then i do the orthogonalization process
did i wrote the orthogonalization formula correctly
??

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#### HallsofIvy

Science Advisor
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)?

#### transgalactic

ok after,
whats the right formula for the orthogonolazation proccess

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

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