Chapter 15: Problem 99
A useful form of the quotient rule for three-dimensional vectors is this: Suppose that a and b are known to be three-vectors and suppose that for every orthogonal set of axes there is a \(3 \times 3\) matrix T with the property that \(\mathbf{b}=\mathbf{T}\) a for every choice of \(\mathbf{a},\) then \(\mathbf{T}\) is a tensor. (a) Prove this. (b) State and prove the corresponding rule for four-vectors and four-tensors.
Short Answer
Step by step solution
Key Concepts
These are the key concepts you need to understand to accurately answer the question.