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:
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