Spectra Realizer | Nonnegative & Stochastic Inverse Eigenvalue Problem

Target Matrix Class

Nonnegative A ≥ 0 Stochastic A ≥ 0, ∑_j A_ij = 1 Symmetric (SNIEP) A = A^T ≥ 0 Symmetric Stochastic A = A^T ≥ 0, ∑_j A_ij = 1

Select the structured matrix cone or manifold to realize your prescribed spectrum.

Target Spectrum σ

Curated Presets Library

Eigenvalues (separated by commas or spaces)

Supports real and complex numbers (e.g., 1, -0.5+0.866i, -0.5-0.866i). Symmetric targets require real eigenvalues.

Numerical Parameters

Tolerance (ε)

Search Effort Profiles

Retries (Restarts) Min 5

Depth (Iters/Retry) Min 1k

Alternating projection restarts with independent random & canonical initializations. Minimum 5 retries and 1,000 depth per attempt.

Realization Matrix A

Spectral Comparison Canvas

Target σ

Realized spec(A)

Unit Circle

Interactive complex plane: Drag to pan, scroll to zoom. Rings indicate target eigenvalues σ, filled dots represent realized eigenvalues of A, and dashed red lines indicate residual discrepancies.

Theoretical Invariant Analysis

Universal necessary conditions governing entrywise nonnegative and stochastic spectral realizations.

Numerical Verification & Invariants

Target vs. Numerical Eigensolver Estimates

Index	Target λ_i	Numerical μ_i	Numerical \|λ_i − μ_i\|

Structured Cone Properties

Property	Measured Value	Status

Numerical Spectra Realizer for Nonnegative and Stochastic Matrices

Analyzing Spectrum...

Target vs. Numerical Eigensolver Estimates

Structured Cone Properties