Inner Products and Inner Product Spaces | Linear Algebra скачать в хорошем качестве

Inner Products and Inner Product Spaces | Linear Algebra

🛍 Check out my math fashion brand! https://mathshion.com/ ❤️ Support the production of this course by joining Wrath of Math to access all my Linear Algebra videos plus lecture notes at the premium tier!    / @wrathofmath   Linear Algebra course:    • Linear Algebra   Linear Algebra exercises:    • Linear Algebra Exercises   Get the textbook for this course! https://amzn.to/45KYgmA Business Inquiries: wrathofmathlessons@gmail.com We introduce inner products and inner product spaces. We'll see how the inner product axioms come directly from the basic properties of the dot product, we'll briefly discuss complex inner product spaces and the symmetry axiom for such spaces, we'll see how norms and distances are defined and calculated in inner product spaces, see examples and non-examples of inner product spaces including an inner product space of matrices, and will see basic algebraic properties of inner products. #linearalgebra Angles and Orthogonality:    • Angles and Orthogonality in Inner Product ...   ★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 Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● Twitter:   / wrathofmathedu   0:00 Intro 1:29 Definition of Inner Product and Inner Product Space 4:26 Euclidean n-Space (with Dot Product) 4:58 Norm and Distance in Inner Product Space 5:45 Properties of Norm and Distance 6:31 Inner Product Non-Example 8:23 Weighted Euclidean Inner Product 11:59 Norm and Distance in Weighted Euclidean Inner Product Space 14:24 Algebraic Properties of Inner Products 17:42 Standard Inner Product on Square Matrices 20:08 Conclusion