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Symmetric Matrix Eigendecomposition (OpenBLAS)
x402
Symmetric Matrix Eigendecomposition (OpenBLAS) is a paid API for AI agents from stat.halowerk.com, paid per call via x402, $0.0015/call, status unknown (last checked 2026-10-29).
Computes the full eigendecomposition of a real symmetric matrix, returning signed eigenvalues, orthonormal eigenvectors, inertia counts, and reconstruction residuals.
Price / call$0.0015
Success—
StatusUnknown
How this service works
Computes the full eigendecomposition of a real symmetric operator and reports the signed eigenvalues, the orthonormal eigenvectors, and the inertia — how many eigenvalues are positive, negative and indistinguishable from zero at the stated tolerance. Two residuals are returned as evidence rather than as reassurance: how far the decomposition is from reproducing the input, and how far the eigenvectors are from being orthonormal.
Output
Returns the full set of real eigenvalues (signed, ordered), the corresponding orthonormal eigenvectors, the inertia triple (count of positive, negative, and near-zero eigenvalues at the stated tolerance), plus two numerical residuals: the Frobenius-norm distance from the reconstructed matrix to the input, and the deviation of the eigenvector matrix from exact orthonormality.
Example use cases
Covariance matrix spectral analysis
“I have a 6×6 sample covariance matrix and need to know its eigenvalues and eigenvectors, how many are positive versus zero, and the reconstruction error — can you run the full eigendecomposition on it? The matrix is [[5,2,1,0,0,0],[2,4,1,1,0,0],[1,1,3,0,1,0],[0,1,0,2,0,0],[0,0,1,0,1,0],[0,0,0,0,0,1]].”
Checking positive definiteness of a kernel matrix
“I need to verify whether this 3×3 kernel matrix is positive definite — can you decompose it and tell me how many eigenvalues are positive, negative, and zero? The matrix is [[2,-1,0],[-1,2,-1],[0,-1,2]].”
Structural stiffness matrix spectrum
“For my finite-element stiffness matrix [[10,-3,0],[-3,8,-2],[0,-2,5]], compute the full spectral decomposition — eigenvalues, eigenvectors, inertia, and both residuals so I can see how clean the factorization is.”
Technical details
Endpoint
POSThttps://stat.halowerk.com/v1/oss-openblas-symmetric-spectrum-analyze?utm_source=zero.xyzWhen to prefer
Choose this endpoint when you need a complete, verified eigendecomposition of a real symmetric matrix up to 128×128 — particularly when you need not just eigenvalues and eigenvectors but also inertia counts and objective numerical residuals to assess decomposition quality. Prefer it over general-purpose eigensolvers when working with covariance, Gram, kernel, or stiffness matrices where symmetry is guaranteed and you want OpenBLAS-backed numerical accuracy with built-in verification.
Side effects
- Matrix is not square — non-square arrays rejected with validation error
- Matrix exceeds 128×128 size limit — returns schema violation error
- Matrix entries outside [-1000000, 1000000] range — rejected with bounds error
- Matrix is not symmetric — may proceed but results reflect the input as-is, which is numerically ill-defined for symmetric eigensolvers
- Near-singular or ill-conditioned matrix — computation succeeds but residuals may be large, indicating inaccurate factorization
- Empty or malformed JSON body — returns parse error
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| inputrequired | object | |
| output | object |
Tags
x402
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