From 06f5d95c983581e92988ac95c6ad2196e1db67b7 Mon Sep 17 00:00:00 2001 From: andy Date: Sun, 21 May 2023 14:49:15 +0100 Subject: [PATCH] vault backup: 2023-05-21 14:49:15 Affected files: .obsidian/plugins/obsidian-git/data.json .obsidian/workspace.json Languages/Spanish.md Languages/Spanish/Verbs.md Politcs/Fascism.md STEM/Images/em-spectrum.png STEM/Images/fermi-vacuum-level.png STEM/Images/photo-electric.png STEM/Light.md STEM/Maths/Tensor.md --- Images/em-spectrum.png | Bin 0 -> 716729 bytes Images/fermi-vacuum-level.png | Bin 0 -> 475471 bytes Images/photo-electric.png | Bin 0 -> 436900 bytes Light.md | 9 ++++++++- Maths/Tensor.md | 26 ++++++++++++++++++++++++++ 5 files changed, 34 insertions(+), 1 deletion(-) create mode 100644 Images/em-spectrum.png create mode 100644 Images/fermi-vacuum-level.png create mode 100644 Images/photo-electric.png create mode 100644 Maths/Tensor.md diff --git a/Images/em-spectrum.png b/Images/em-spectrum.png new file mode 100644 index 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a/Light.md +++ b/Light.md @@ -7,4 +7,11 @@ $$E=hf$$ 1. The maximum KE of ejected electrons is independent of intensity, but dependent on frequency $n$ 2. There is a minimum frequency n0below which there is no emission -3. No time delay (less than 1 ns) before the onset of emission –but the rate of electrons depends on the intensity. \ No newline at end of file +3. No time delay (less than 1 ns) before the onset of emission –but the rate of electrons depends on the intensity. + +![[photo-electric.png]] +![[fermi-vacuum-level.png]] + +![[em-spectrum.png]] +- Radio spectrum + - 30Hz – 300 GHz \ No newline at end of file diff --git a/Maths/Tensor.md b/Maths/Tensor.md new file mode 100644 index 0000000..61d5e54 --- /dev/null +++ b/Maths/Tensor.md @@ -0,0 +1,26 @@ +## 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 +![[tensor.png]] +# Transformation Rules + +1. Transforms like a tensor +2. Invariant to a change in coordinate system + - Components change according to mathematical formulae + +## Dimension +- Dimensionality to the rank = number of components + +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 + +From <[wolfram](https://mathworld.wolfram.com/Tensor.html)> \ No newline at end of file

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