andy
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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
850 B
850 B
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>