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
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874 B
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Rank
- Number of indices
- Basis vectors per dimension/component
- 0
- Scalar
- 1
- Column Vector
- 2
- Square Matrix
- 3
- Cube matrix
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
Transformation Rules
- Transforms like a tensor
- Invariant to a change in coordinate system
- Components change according to mathematical formulae
Dimension
- Dimensionality to the rank = number of components
An $n$-rank tensor in $m$-dimensional space is a mathematical object that has n indices and m^n components and obeys certain transformation rules
From <wolfram>