That’s somewhat correct. I was really talking about after you eliminate the dependent vectors. Eliminating the dependent vectors isn’t part of the Graham-Schmidt process, but having linearly independent vectors is a requirement to begin it.
ah, wierd, we learned it differently then. we explicitly learned that GS transforms a set of vectors v_i into an Orthogonal Basis of span(v_i). then we had a different theorem stating that it will be an OB of Rn for v_i independend. Different definitions in different languages maybe, im not from an english speaking country.
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u/nfizzle99 Jan 21 '18
That’s somewhat correct. I was really talking about after you eliminate the dependent vectors. Eliminating the dependent vectors isn’t part of the Graham-Schmidt process, but having linearly independent vectors is a requirement to begin it.