Lucy's mathematical toy / Certification protocol

Planned
VISUALIZATION SLOT

The geometry for this step will be built here.

Not built yet
Reserved for the interactive scene
Interactive controlsAdded when we develop this step.

Abstract 2 × 2 toy · All 13 pages available · Animations illustrate the supplied toy data

SHARED REFERENCE

Notation & toy data

Actual contour minima, certified lower bounds and pointwise values have different roles. The quantities relevant to each step also appear beside that step.

a∘ ≤ sΓ(A2∘) ≤ a∗

A certified lower bound, the actual contour minimum, and one pointwise SVD value.

The contour and midpoint

c = 5/8 + i/4   ·   δ = 1/16

U = { z ∈ ℂ : |z − c| < δ },   Γ = ∂U

A2∘ =
1/2 + i/43/8 − i/81/16 + i/81/4 − i/16

Four different spaces

Spectral plane ℂ ≅ ℝ²Matrix space ℂ²ˣ² ≅ ℝ⁸Finite vector space ℂ² ≅ ℝ⁴Lifted vector space ℂ³ ≅ ℝ⁶

An underline denotes a certified lower bound. Plain U is the spectral disk; U∗ denotes an SVD frame. Reference data are not a new numerical validation.