Manuscript VI-B@1 · VI-B-v1.tex · proposition · 33798723

Proposition: Approximate annihilation needs coefficient bounds

Finite certificates and their logical limits · lines 1370–1384 · proof included or linked

VI-B@1#prop:approximate

If $z^{T} N_{S} \neq = 0$ , then

c \in R^{L} sup ∣ z^{T} N_{S} c ∣ = \infty.

If instead $∥ c ∥ \leq C$ , the residual is bounded by $C z^{T} N_{S}$ in dual norms.

Proof. Scale any $c_{0}$ for which $z^{T} N_{S} c_{0} \neq = 0$ . The bounded assertion is the dual norm inequality.

Displayed formulas in this passage