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/