Computations with Weighted Euclidean Inner Product | Linear Algebra Exercises

We go over several examples of basic computations in an inner product space with respect to a weighted euclidean inner product on R^2. We compute weighted Euclidean inner products, we use the additivity property, compute distance in the inner product space, and compute the norm of a vector in the space using the inner product. #linearalgebra

Inner Products and Inner Product Spaces: (coming soon)

Linear Algebra course:    • Linear Algebra  
Linear Algebra exercises:    • Linear Algebra Exercises  

Join Wrath of Math to get exclusive videos, music, and more:
   / @wrathofmath  

0:00 Intro
0:38 Weighted Euclidean Inner Product
1:15 Scalar times Inner Product
1:55 Additivity Inner Product
3:03 Norm with Inner Product
4:00 Distance in Inner Product Space
5:05 Norm of Scaled Vector
5:48 Conclusion

◉Textbooks I Like◉
Graph Theory: https://amzn.to/3JHQtZj
Real Analysis: https://amzn.to/3CMdgjI
Abstract Algebra: https://amzn.to/3IjoZaO
Linear Algebra: https://amzn.to/43xAWEz
Calculus: https://amzn.to/3PieD1M
Proofs and Set Theory: https://amzn.to/367VBXP (available for free online)
Statistics: https://amzn.to/3tsaEER
Discrete Math: https://amzn.to/3qfhoUn
Number Theory: https://amzn.to/3JqpOQd

★DONATE★
◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits:   / wrathofmathlessons  
◆ Donate on PayPal: https://www.paypal.me/wrathofmath

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:   / wrathofmathedu  
● Facebook:   / wrathofmath  
● Twitter:   / wrathofmathedu  

My Math Rap channel:    / @mathbars2020