Cross products in the light of linear transformations: Essence of Linear Algebra - Part 11 of 15

The video tutorial explains the computation and geometric interpretation of the 3D cross product. It begins with an introduction to the cross product and its properties, such as the right-hand rule. The concept of duality and its relation to linear transformations is discussed, followed by a comparison of 2D and 3D cross product calculations. The tutorial defines a function from three dimensions to the number line and explores the dual vector associated with this transformation. Finally, it provides a geometric understanding of the cross product, emphasizing the relationship between computation and geometry.

Explain how the cross product can be interpreted geometrically.

What does it mean for a function to be linear in the context of the cross product?

How can the computation of the cross product be related to the dot product?

Summarize the key points that connect the computational and geometric interpretations of the cross product.