A Sharp Condition-Number Bound for a Tetrahedral Observation Operator
Year: 2026
Type: preprint
Abstract: This paper proves a sharp global condition-number bound for a finite-dimensional tetrahedral observation operator. For every ordered triple of unit directions (n_1,n_2,n_3), the associated two-block Gramian satisfies \kappa_2(G)\ge 30. The bound is sharp, and equality is completely classified: \kappa_2(G)=30 exactly when n_1 is a signed coordinate axis and n_2,n_3 are signed coordinate axes on two distinct underlying coordinate axes. The proof is finite-dimensional and uses tetrahedral coordinates, Rayleigh quotients, a 3\times3 symmetric reduction, and exact equality analysis.
Author: Bulgaretti, Silvio
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212419129
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