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
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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
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I really enjoy your videos. Your videos are clean and easy to follow step by step with no unnecessary explanations to confuse and no omissions of necessary explanations!

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Thanks so much, I work hard to deliver exactly that!

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Very clear explanation ! Thank you Sir !

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You are welcome!

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bro's carrying my linear algebra GPA

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Gotta do my part