Linear transformations and bases

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In this video, we prove that every linear transformation can be uniquely defined by prescribing arbitrary values on any basis. We also show how to construct a linear transformation that has been defined on a basis only.

This video is part of a linear algebra course
https://www.youtube.com/playlist?list=PLxQVx0jlffqfMhwn-i9q161gGxURlk7wb

I recommend the following open source book as companion text to this linear algebra video course: http://linear.ups.edu/

Students often ask is linear algebra important and is linear algebra hard. They wonder can anyone learn linear algebra and why some can't understand linear algebra. It is important to show to the students how linear algebra is used in data science, machine learning, AI, computer science, image processing, computer graphics, and in real life in general. This is a free video course in linear algebra for everyone, even beginners. It covers linear algebra with applications.

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