4.1. Multiplication of a second order tensor with a vector

Try these first

1. 1.

   Define a second order tensor.

   Hint

   Think of the relationship with matrices.

2. 2.

   What is the Kronecker delta function?

   Hint

   Recall its role in filtering terms during summation.

3. 3.

   What does the product of a second order tensor and a vector yield?

   • A scalar
   • Another vector
   • A matrix

   Hint

   Remember the dimensionality of the result.

4. 4.

   True or False: The Kronecker delta is used in tensor operations to filter relevant components.

   • True
   • False

   Hint

   Think about how the delta behaves with equal indices.

5. 5.

   Given tensor C = [[3, -1], [2, 4]] and vector b = [6, 5], find the resultant vector a and interpret the effect.

   Hint

   Break down each component operation.

6. 6.

   Illustrate how the multiplication of a second order tensor is essential in engineering analyses.

   Hint

   Think about loading conditions or structural bending.