Manuscript En08-A@1 · En08-A.tex · corollary · c688d76d

Corollary: Application to records

Signature and Lorentz-cone selection › The symmetric-cone representation theorem · lines 1412–1428 · proof included or linked

En08-A@1#cor:networkrepresentation

Back to manuscript

Under the hypotheses of Theorem thm:mainpositive,

p ⇝ q ⟺ T (ι (q) - ι (p)) \in L_{m} (p \neq = q) .

Proof. Theorem thm:network identifies sensitivity with strict reachability, (eq:orderfaithful) identifies reachability with the restricted cone order, and Theorem thm:representation identifies that cone with $L_{m}$ .

Displayed formulas in this passage

unlabeled · line 1415
$p ⇝ q ⟺ T (ι (q) - ι (p)) \in L_{m} (p \neq = q) .$

Nearby in this section

definition: Definition: Faces and strict convexity of a cone
section: The symmetric-cone representation theorem
assumption: Assumption: Symmetric-cone selection axiom
section: The symmetric-cone representation theorem
theorem: Theorem: Representation from cone order and
corollary: Corollary: Exclusion of the polyhedral realizations
section: The symmetric-cone representation theorem
figure: Figure