I am studying the book Linear Algebra from Hoffman and Kunze. The authors make the following comment on page 281.
Although it is of limited practical use for computations, it is interesting to note that the Gram-Schmidt process may also be used to test for linear dependence.
I have two question on that comment:
1) Why should I study the Gram-Schmidt orthogonalization process?
2) Is there an example where the Gram-Schmidt orthogonalization process makes easier to prove that a set of vectors is linearly dependent instead of use another method? I've never proved that a subset of vectors was linearly independent by using the Gram-Schmidt orthogonalization process.
Maybe I did not understand what they are saying.