26 lines
837 B
Markdown
26 lines
837 B
Markdown
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## Rank
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- Number of indices
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- Basis vectors per dimension/component
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- 0
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- Scalar
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- 1
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- Column Vector
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- 2
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- Square Matrix
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- 3
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- Cube matrix
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Matrices are not inherently rank-2 tensors. Matrices are just the formatting structure. The tensor described by the matrix must follow the transformation rules to be a tensor
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![[tensor.png]]
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# Transformation Rules
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1. Transforms like a tensor
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2. Invariant to a change in coordinate system
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- Components change according to mathematical formulae
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## Dimension
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- Dimensionality to the rank = number of components
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An $n$-[rank](https://mathworld.wolfram.com/TensorRank.html) tensor in $m$-dimensional space is a mathematical object that has $n$ indices and $m^n$ components and obeys certain transformation rules
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From <[wolfram](https://mathworld.wolfram.com/Tensor.html)>
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