Cross products in the light of linear transformations | Essence of linear algebra chapter 11

Stolen from https://youtube.com/watch?v=BaM7OCEm3G0 (August 31, 2016)

Home page: https://www.3blue1brown.com/​
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.

Full series: http://3b1b.co/eola​

Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced.
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