General Linear Transformations on Vector Spaces | Linear Algebra скачать в хорошем качестве

General Linear Transformations on Vector 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 general linear transformations on vector spaces. This is in contrast to matrix transformations which represented the class of linear transformations specifically on euclidean space. We'll go over the definition of a linear transformation, some basic properties of linear transformations, and several linear transformation examples and non-examples. #linearalgebra Matrix Transformations and Linear Transformations:    • Matrix Transformations and Linear Transfor...   ★DONATE★ ◆ Support Wrath of Math on Patreon:   / wrathofmathlessons   ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● TikTok:   / wrathofmathedu   ● X: https://x.com/wrathofmathedu 0:00 Intro 1:16 Definition of Linear Transformation 2:26 Linear Combinations 3:10 Basic Properties 4:01 Proofs of Basic Properties 6:23 Matrix Transformation 7:36 Zero Transformation 9:14 Dilation and Contraction 11:13 Inner Product Transformation 12:59 Matrix Transformation 14:18 sinx is not a Linear Transformation 15:06 Translation is not a Linear Transformation 16:37 Conclusion