General Linear Transformations on Vector Spaces

Offered By: Wrath of Math via YouTube

Course Description

Overview

Save Big on Coursera Plus. 7,000+ courses at $160 off. Limited Time Only!

Explore general linear transformations on vector spaces in this 17-minute video lecture. Learn the definition of linear transformations, their basic properties, and how they differ from matrix transformations specific to Euclidean space. Examine various examples and non-examples of linear transformations, including zero transformation, dilation and contraction, inner product transformation, and matrix transformation. Understand why functions like sinx and translation are not linear transformations. Gain insights into linear combinations and proofs of basic properties to deepen your understanding of linear algebra concepts.

Syllabus

Intro
Definition of Linear Transformation
Linear Combinations
Basic Properties
Proofs of Basic Properties
Matrix Transformation
Zero Transformation
Dilation and Contraction
Inner Product Transformation
Matrix Transformation
sinx is not a Linear Transformation
Translation is not a Linear Transformation
Conclusion

Taught by

Wrath of Math

Related Courses

First Steps in Linear Algebra for Machine Learning
Higher School of Economics via Coursera Vanessa Robins - The Extended Persistent Homology Transform for Manifolds with Boundary
Applied Algebraic Topology Network via YouTube Johnathan Bush - Maps of Čech and Vietoris–Rips Complexes into Euclidean Spaces
Applied Algebraic Topology Network via YouTube Convex Sunflower Theorems and Neural Codes
Applied Algebraic Topology Network via YouTube Borsuk-Ulam Theorems into Higher-Dimensional Codomains
Applied Algebraic Topology Network via YouTube