Cross products in the light of linear transformations
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Video Lecture 12 of 15
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Date Added: May 13, 2017

### Lecture Description

For anyone who wants to understand the cross product more deeply, this video shows how it relates to a certain linear transformation via duality. This perspective gives a very elegant explanation of why the traditional computation of a dot product corresponds to its geometric interpretation.

*Note, in all the computations here, I list the coordinates of the vectors as columns of a matrix, but many textbooks put them in the rows of a matrix instead. It makes no difference for the result, since the determinant is unchanged after a transpose, but given how I've framed most of this series I think it is more intuitive to go with a column-centric approach.

Watch the full "Essence of linear algebra" playlist here: goo.gl/R1kBdb

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### Course Description

This introduces the "Essence of Linear Algebra" series, aimed at animating the geometric intuitions underlying many of the topics taught in a standard linear algebra course.

This course is perfect for any high school student interested in exploring the world of Linear Algebra, which any math and engineering student will face in their college years. Furthermore, this course is perfect for any university and adult learner who wants an intuitive, original, and entertaining explanation of simple and complex Linear Algebra concepts.