Andy Pack
c3ebefdd64
Affected files: .obsidian/workspace.json Food/Plans & Recipes.canvas Health/ADHD.md Health/Alexithymia.md Health/Anxiety.md Health/BWS.md Health/Worry Tree.md History/Britain.md Media/Listen.md Media/Watch.md Money/Assets/Asset.md Money/Assets/CFD.md Money/Assets/Derivative.md Money/Assets/Financial Instruments.md Money/Assets/Options.md Money/Assets/Security.md Money/Assets/Stocks.md Money/Econ.md Money/Equity.md Money/Inflation.md Money/Markets/Commodity.md Money/Markets/Markets.md Money/Markets/Types.md Money/Prices.md Money/To Learn.md Politcs/British/Prime Ministers.md Politcs/British/Tory.md Politcs/Neoliberalism/Thatcher.md Politcs/Now.md Projects/Dev Options.md STEM/AI/Neural Networks/Activation Functions.md STEM/AI/Neural Networks/MLP/Back-Propagation.md STEM/AI/Neural Networks/SLP/Least Mean Square.md STEM/AI/Pattern Matching/Markov/Markov.md STEM/Maths/Algebra.md STEM/Maths/Tensor.md STEM/Maths/Vector Operators.md Want/Clothes.md Want/House.md Want/Want.md Work/Board.canvas
30 lines
874 B
Markdown
30 lines
874 B
Markdown
---
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tags:
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- maths
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---
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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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# 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)> |