Wrath of Math | Composition of Linear Transformations | Linear Algebra @WrathofMath | Uploaded 1 month ago | Updated 12 hours ago
We introduce the composition of linear transformations, how composition of transformations is defined, we prove that the composition of linear transformations is a linear transformation, we go over an example of a composition of linear transformations, discuss compositions of multiple transformations, and prove that a composition of one to one transformations is a one-to-one transformation and that the inverse of a composition of transformations is the composition of the inverses in reverse order. #linearalgebra

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0:00 Intro
0:28 Definition of Composition of Linear Transformations
2:04 Composition of Linear Transformations is Linear
5:59 Order of Composition
6:22 Example of Composition of Transformations
9:42 Composition of Many Transformations
10:42 One to One and Inverse Theorem
11:23 Proof Composition is One to One
12:42 Proof for Inverse Formula
15:59 Conclusion

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