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If types are omitted then there's actual missing information from the equation. If summations are omitted, there... isn't. They add nothing (at least in relativ
by ajkjk 8y ago
If types are omitted then there's actual missing information from the equation. If summations are omitted, there... isn't. They add nothing (at least in relativity where every sum is over the same 4 values).
Anyway, index notation is more of a shorthand for symbolic tensor algebra computations than actual sums. The problem is that when dealing with 2, 3, and 4 index tensors, with co- and contra-variant indexes, it's quite cumbersome to notate which component of a tensor contracts with which component of another tensor, and anything you could come up with would end up looking like index notation. Rarely do you actually mean to sum anything.
- joppy 8y agoI don't have a problem with using indices for anything, they are fine. Distinguishing upper and lower indices is even better. The exact complaint I have is the implicit sums. For example, a matrix A would be written with one upper and one lower index, which I'll just write as A[i, j]. In einstein (implicit sum) notation, the trace of the matrix is written Tr A = A[i, i]. Is this really better than saying Tr A = Sum[i] A[i, i]?