11. When using multi-index notation , an underarrow is placed underneath the block of indices: 12. The index notation for the dot and cross products carries over to the differential operators of vector calculus. 13. Where C _ { abcd } is the Weyl tensor, and we used the abstract index notation . 14. It is denoted in coordinate-free notation using ?" and components are defined in index notation by: 15. Index notation is often the clearest way to express definitions, and is used as standard in the literature.16. Generally, the first is used in simpler contexts, while index notation is used to make advanced manipulations simpler. 17. The notation used here is commonly used in statistics and engineering, while the tensor index notation is preferred in physics. 18. A more general notation is tensor index notation , which has the flexibility of numerical values rather than fixed coordinate labels. 19. The abstract index notation denotes tensors as if they were represented by their coefficients with respect to a fixed local tetrad. 20. The second column expands each term in index notation ( neglecting the proper normalization coefficient ) . and are the generation indices.
