2.3. Tensor Product

Try these first

1. 1.

   What is the tensor product of vectors A = [1,2] and B = [3,4]?

   Hint

   Multiply corresponding components.

2. 2.

   What is a second order tensor?

   Hint

   Think of it as a matrix of components.

3. 3.

   What does the tensor product of two vectors produce?

   • Another vector
   • A second order tensor
   • A scalar

   Hint

   Recall the operation we performed earlier.

4. 4.

   True or False: The representation of a tensor changes with coordinate transformations.

   • True
   • False

   Hint

   Think about how coordinates influence vector representations.

5. 5.

   Given two vectors A = [1, 2] and B = [3, 4], compute the tensor C = A ⊗ B and explain the meaning of each element in terms of interaction.

   Hint

   Consider the significance of each product and how they illustrate combined vector magnitudes.

6. 6.

   Define a physical situation where a third order tensor could apply, and compute its elements if A = [1, 0, 2] and B = [0, 3, 4].

   Hint

   Think of the interactions that could occur in three dimensions.