Introduction to "Pointwise Qualitative Factorization of 2-forms into 1-forms over R4

Introduction to "Pointwise Qualitative Factorization of 2-forms into 1-forms over ℝ⁴, PDF format; 175K.

I just know Calculus III, or calculus-based physics. Does this paper have any use whatsoever to me?

Then you should know about the cross product ×, and know what to feed into a four-function calculator to compute it:

(a₁, a₂, a₃)×(b₁, b₂, b₃) = (a₂b₃-a₃b₂, a₃b₁-a₁b₃, a₁b₂-a₂b₁)

If you have memorized the formula in x-y-z coordinates, just change the subscripts from x,y,z to 1,2,3 to convert. The coordinate formulation should look very similar to the coefficients I defined in the paper...in fact, the second part rewrites (in the paper's notation) to

(c₂₃, -c₁₃, c₁₂)

There's some "stratosphere math" that explains how things are defined so this works out. Rather than go into that here, just use the result:

We can rephrase the entire paper to talk about making inferences about coordinates a_1..4, b_1..4 from the coordinates of the four cross-products

(a₁, a₂, a₃)×(b₁, b₂, b₃) = (c₂₃, -c₁₃, c₁₂)
(a₁, a₂, a₄)×(b₁, b₂, b₄) = (c₂₄, -c₁₄, c₁₂)
(a₁, a₃, a₄)×(b₁, b₃, b₄) = (c₃₄, -c₁₄, c₁₃)
(a₂, a₃, a₄)×(b₂, b₃, b₄) = (c₃₄, -c₂₄, c₂₃)

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