Скачать с ютуб Orthogonal and Orthonormal Bases | Linear Algebra в хорошем качестве

Orthogonal and Orthonormal Bases | Linear Algebra

We introduce orthogonal bases and orthonormal bases for inner product spaces. We'll prove an important theorem stating orthogonal sets of vectors are linearly independent, and see several examples of orthogonal and orthonormal bases. We'll also prove a theorem telling us how to write a vector as a linear combination of orthogonal basis vectors. #linearalgebra Orthogonal and Orthonormal Sets:    • Orthogonal and Orthonormal Sets in In...   Join Wrath of Math to get exclusive videos, music, and more:    / @wrathofmath   Linear Algebra course:    • Linear Algebra   Linear Algebra exercises:    • Linear Algebra Exercises   0:00 Intro 0:25 Definition of Orthogonal and Orthonormal Sets 0:56 Linear Independence of Orthogonal Sets 4:58 Definition of Orthogonal and Orthonormal Bases 5:32 Orthonormal Basis for R^n 6:03 Orthonormal Basis for Pn 7:50 Non-standard Orthonormal Basis for R^3 8:37 Writing a Vector as a Linear Combination of Orthonormal Basis Vectors 10:28 Proof for Orthonormal Basis Expression 13:26 Coordinate Vector Relative to Orthonormal Basis 16:20 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