Tensor

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Full Title or Meme

Tensors are the most efficient packaging device we have to organize our equations. They’re the natural language for geometric objects.” - Dionysios Anninos, a theoretical physicist at King’s College London[1]

Context

  • See the wiki page on Matrix Calculation for ideas about where Tensors work.
  • Einstein in 1915 found the simple-looking formula that describes General Relativity in a new geometric theory described a few years before by the Italian mathematicians Gregorio Ricci-Curbastro and Tullio Levi-Civita of a new structure for the mathematical foundation that would later be dubbed a “tensor.”
  • Tensors are simple in concept - just an array of numbers. A single number is a “rank 0” tensor. A list of numbers, called a vector, is a rank 1 tensor. A grid of numbers, or matrix, is a rank 2 tensor. And so on.
  • What makes tensors interesting is the way that they are used to transform one type of structure into another.

References

  1. Joseph Howlett, The Geometric Tool That Solved Einstein’s Relativity Problem Quanta (2024-08-12) https://www.quantamagazine.org/the-geometric-tool-that-solved-einsteins-relativity-problem-20240812/