Affiliation:
1. Dipartimeno di Matematica Università di Roma “Tor Vergata” Rome Italy
Abstract
We show that the gradient of a strongly differentiable function at a point is the limit of a single coordinate‐free Clifford quotient between a multidifference pseudo‐vector and a pseudo‐scalar, or of a sum of Clifford quotients between scalars (as numerators) and vectors (as denominators), both evaluated at the vertices of a same non‐degenerate simplex contracting to that point. Such result allows to fix an issue with a defective definition of pseudo‐scalar field in Sobczyck's simplicial calculus. Then, we provide some consequences and conjectures implied by the foregoing results.
Subject
General Engineering,General Mathematics
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