We go over orthogonal projections onto subspaces of inner product spaces. We'll see the projection theorem, telling us that - given a finite dimensional subspace W of an inner product space V, we can decompose any vector u from V into a vector in W plus a vector in the orthogonal complement W perp. We'll prove and use a theorem telling us how to calculate the orthogonal projection of a vector onto a subspace and how to calculate the component of a vector orthogonal to a subspace.
Orthogonal and Orthonormal Bases: • Orthogonal and Orthono...
Linear Algebra course: • Linear Algebra
Linear Algebra exercises: • Linear Algebra Exercises
Join Wrath of Math to get exclusive videos, music, and more:
/ @wrathofmath
◉Textbooks I Like◉
Graph Theory: amzn.to/3JHQtZj
Real Analysis: amzn.to/3CMdgjI
Abstract Algebra: amzn.to/3IjoZaO
Linear Algebra: amzn.to/43xAWEz
Calculus: amzn.to/3PieD1M
Proofs and Set Theory: amzn.to/367VBXP (available for free online)
Statistics: amzn.to/3tsaEER
Discrete Math: amzn.to/3qfhoUn
Number Theory: amzn.to/3JqpOQd
★DONATE★
◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits: / wrathofmathlessons
◆ Donate on PayPal: www.paypal.me/...
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
5 сен 2024