We introduce the definition of orthogonal sets and orthonormal sets in inner product spaces. An orthogonal set is a set of vectors which are all orthogonal to each other with respect to the inner product in question, if the norm of each vector in an orthogonal set is 1, then the set is called orthonormal. We'll see an orthogonal set in R^3, convert it to an orthonormal set, then see a theorem concerning the linear independence of orthogonal sets. We'll finishes with bases. #linearalgebra

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0:00 Intro
0:36 Definition of Orthogonal and Orthonormal Set
1:03 Orthogonal Set in R^3
2:10 Converting to Orthonormal Set
4:25 Linear Independence of Orthogonal Sets
5:31 Standard Orthonormal Basis for R^3
5:51 Conclusion

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