Dot Products and Duality | Essence of Linear Algebra, Chapter 7

The dot product of two matrices is a number on the number line, its transformation. The resource presents the dot product as a linear transformation from two dimensions to one dimension. The video uses the numerical and graphical interpretations of vectors to make its point in the tenth installment of a 15-part series.

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CCSS: Adaptable
Instructional Ideas

  • Lead a discussion on how one might be able to calculate the projection of one vector onto another
  • Verify the claim about the sign of the dot product and the relative orientation of the two vectors
Classroom Considerations

  • It may be beneficial if the class already knows how to calculate a dot product
Pros

  • Introduces new concepts by building upon previous knowledge
  • Includes an example to help clarify the concept
Cons

  • None
Common Core