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

Why the formula for cross products matches the geometric intuition.

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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.

Minor error at 1:44, the third line of the matrix should read "v1 * w2 - w1 * v2"

*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.

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Thanks to these viewers for their contributions to translations

Hebrew: Omer Tuchfeld

Vietnamese: @ngvutuan2811

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