General Linear Transformations on Vector Spaces | Linear Algebra

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

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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

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Outro music by Ben Watts and is available for channel members.

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