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