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

Linear Algebra course: [ Ссылка ]
Linear Algebra exercises: [ Ссылка ]

Join Wrath of Math to get exclusive videos, music, and more:
[ Ссылка ]

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

◉Textbooks I Like◉
Graph Theory: [ Ссылка ]
Real Analysis: [ Ссылка ]
Abstract Algebra: [ Ссылка ]
Linear Algebra: [ Ссылка ]
Calculus: [ Ссылка ]
Proofs and Set Theory: [ Ссылка ] (available for free online)
Statistics: [ Ссылка ]
Discrete Math: [ Ссылка ]
Number Theory: [ Ссылка ]

★DONATE★
◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits: [ Ссылка ]
◆ Donate on PayPal: [ Ссылка ]

Thanks to Loke Tan, Raül Beienheimer, Matt Venia, Micheline, Doug Walker, Odd Hultberg, Marc, Shlome Ashkenazi, Barbora Sharrock, Mohamad Nossier, Rolf Waefler, Shadow Master, and James Mead for their generous support on Patreon!

Outro music is mine. You cannot find it anywhere, for now.

Follow Wrath of Math on...
● Instagram: [ Ссылка ]
● Facebook: [ Ссылка ]
● Twitter: [ Ссылка ]

My Math Rap channel: [ Ссылка ]

свернуть