【金-元】元好问

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【金-元】元好问

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This note explains how infinitesimal changes transform under coordinate maps via the Jacobian matrix—from differential displacement to differential area and volume—in Cartesian, cylindrical, and spherical coordinates.

Note: Everything here is 3D and the cross product is used. In general dimensions, area/volume elements are best expressed using differential forms (wedge products); the 3D vector formulas here are a special case.

Sources:

  1. Fawwaz Ulaby. (2020). Chapter 3: Vector Analysis. Fundamentals of applied electromagnetics (8rd ed., pp. 130–163). Pearson.
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Sources:

  • Fawwaz T. Ulaby & Umberto Ravaioli. (2020). Chapter 1. Introduction: Waves and Phasors. Fundamentals of Applied Electromagnetics (8th ed., pp. 22-30). Pearson.
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Sources:

  • VICReg 2022 paper
  • VC Reg, a follow-up paper of VICReg
VCReg which is quite similar to VICeg

Image source: https://arxiv.org/pdf/2306.13292

# TODO: This note is flawed and I'll rewrite it in future.

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