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Results tagged with tensor-calculus
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user 21270
Tensor calculus (tensor analysis) is a systematic extension of vector calculus to multivector and tensor fields in a form that is independent of the choice of coordinates on the relevant manifold, but which accounts for respective sub-spaces, their symmetries, and their connections.
3
votes
1
answer
2k
views
Transformation rule of a partial derivative
We know the following transformation rule:
$$ \partial'_b = \frac{\partial}{\partial x'^b} = \frac{\partial x^c}{\partial x'^b} \, \frac{\partial}{\partial x^c} = \frac{\partial x^c}{\partial x'^b} \ …
- 3,053
5
votes
3
answers
4k
views
Square bracket notation for anti-symmetric part of a tensor
I know that
$A_{[a} B_{b]} = \frac{1}{2!}(A_{a}B_{b} - A_{b}B_{a})$
But how can write $E_{[a} F_{bc]}$ like the above?
Can you provide a reference where this notational matter is discussed?
- 3,053