Matrix Transformations and Linear Transformations | Linear Algebra

We introduce matrix transformations and their equivalence with linear transformations from R^n to R^m. We'll give examples of linear transformations, see some important properties of matrix transformations including the homogeneity property and additivity properties. We'll also see functions that aren't matrix transformations and we will prove they aren't matrix transformations. We finish by going over how to find the standard matrix for a linear transformation. #linearalgebra

Linear Algebra course:    • Linear Algebra  
Linear Algebra exercises:    • Linear Algebra Exercises  

Join Wrath of Math to get exclusive videos, music, and more:
   / @wrathofmath  

0:00 Intro
0:20 What is a Matrix Transformation
4:45 Example of Matrix Transformation
6:30 Properties of a Matrix Transformation
7:58 Transformations of Linear Combinations
8:46 Non-Examples of Matrix Transformations
10:58 Two Key Questions
11:23 Homogeneity and Additivity
11:49 Linear Transform
12:30 Finding Standard Matrix for a Linear Transformation
13:35 Standard Matrix Example
15:15 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