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Affected files: Money/Assets/Financial Instruments.md Money/Assets/Security.md Money/Markets/Markets.md Politcs/Now.md STEM/AI/Neural Networks/CNN/Examples.md STEM/AI/Neural Networks/CNN/FCN/FCN.md STEM/AI/Neural Networks/CNN/FCN/FlowNet.md STEM/AI/Neural Networks/CNN/FCN/Highway Networks.md STEM/AI/Neural Networks/CNN/FCN/ResNet.md STEM/AI/Neural Networks/CNN/FCN/Skip Connections.md STEM/AI/Neural Networks/CNN/FCN/Super-Resolution.md STEM/AI/Neural Networks/CNN/GAN/DC-GAN.md STEM/AI/Neural Networks/CNN/GAN/GAN.md STEM/AI/Neural Networks/CNN/GAN/StackGAN.md STEM/AI/Neural Networks/CNN/Inception Layer.md STEM/AI/Neural Networks/CNN/Interpretation.md STEM/AI/Neural Networks/CNN/Max Pooling.md STEM/AI/Neural Networks/CNN/Normalisation.md STEM/AI/Neural Networks/CNN/UpConv.md STEM/AI/Neural Networks/CV/Layer Structure.md STEM/AI/Neural Networks/MLP/MLP.md STEM/AI/Neural Networks/Neural Networks.md STEM/AI/Neural Networks/RNN/LSTM.md STEM/AI/Neural Networks/RNN/RNN.md STEM/AI/Neural Networks/RNN/VQA.md STEM/AI/Neural Networks/SLP/Least Mean Square.md STEM/AI/Neural Networks/SLP/Perceptron Convergence.md STEM/AI/Neural Networks/SLP/SLP.md STEM/AI/Neural Networks/Transformers/LLM.md STEM/AI/Neural Networks/Transformers/Transformers.md STEM/AI/Properties.md STEM/CS/Language Binding.md STEM/Light.md STEM/Maths/Tensor.md STEM/Quantum/Orbitals.md STEM/Quantum/Schrödinger.md STEM/Quantum/Standard Model.md STEM/Quantum/Wave Function.md Tattoo/Music.md Tattoo/Plans.md Tattoo/Sources.md
26 lines
850 B
Markdown
26 lines
850 B
Markdown
## 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)> |