index notation वाक्य
उदाहरण वाक्य
मोबाइल
- In the corresponding tensor index notation, the above matrix expression is
- If is any four-vector, then in tensor index notation
- Applying the multi-index notation the Taylor series for several variables becomes
- In abstract index notation, the EFE reads as follows:
- The function, matrix, and index notations all mean the same thing.
- All tensors are written in abstract index notation.
- Index notation allows one to display permutations in a way compatible with tensor analysis:
- These are expressed in index notation as:
- Order the monomials in the variables multi-index notation for monomials in the variables.
- Penrose would also introduce abstract index notation.
- When using multi-index notation, an underarrow is placed underneath the block of indices:
- The index notation for the dot and cross products carries over to the differential operators of vector calculus.
- Where C _ { abcd } is the Weyl tensor, and we used the abstract index notation.
- It is denoted in coordinate-free notation using ?" and components are defined in index notation by:
- Index notation is often the clearest way to express definitions, and is used as standard in the literature.
- Generally, the first is used in simpler contexts, while index notation is used to make advanced manipulations simpler.
- The notation used here is commonly used in statistics and engineering, while the tensor index notation is preferred in physics.
- A more general notation is tensor index notation, which has the flexibility of numerical values rather than fixed coordinate labels.
- The abstract index notation denotes tensors as if they were represented by their coefficients with respect to a fixed local tetrad.
- The second column expands each term in index notation ( neglecting the proper normalization coefficient ) . and are the generation indices.
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