Practice Second Order Tensors And Their Representation (3) - A vector and its representation

Practice: Second order tensors and their representation

Lesson 3A vector and its representation

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8 questions

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6 questions · about 4 min · pass mark 70%. Hints available.
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2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is a second-order tensor?
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Think of it as a complex form of a vector.
Question 2.
Give an example of a basis tensor.
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What builds the structure of a tensor?
3Question 3.
What type of mathematical object is a second-order tensor?
- A scalar
- A vector
- A matrix
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Consider how tensors build upon the structure of vectors.
4Question 4.
True or False? The representation of a tensor can change while the tensor itself remains the same.
- True
- False
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Think about what happens when you rotate your viewpoint on an object.
Question 5.
Given two vectors A and B, define their second-order tensor and its representation in a coordinate system. Then transform it to a new coordinate system after rotating it by 45 degrees.
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Use the formula for the rotation matrix to aid your transformations.
Question 6.
Consider two different second-order tensors T1 and T2. Describe the procedure to multiply them and express the resulting tensor’s components.
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Focus on how the tensor indices interact when multiplied.

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