Cross products in the light of linear transformations. Essence of linear algebra chapter 8 part 2

Ссылка на оригинальное видео: Оригинальное описание: 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: ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and c