# Symmetric Matrix Eigendecomposition (OpenBLAS)

> 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.

## Facts

- Endpoint: POST https://stat.halowerk.com/v1/oss-openblas-symmetric-spectrum-analyze?utm_source=zero.xyz
- Price: $0.0015/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-29
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/symmetric-matrix-eigendecomposition-openblas-622f9a6e
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_S89BdlwcfS94vLFfWr8yP

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability symmetric-matrix-eigendecomposition-openblas-622f9a6e -d '<json body>'
```

Example prompt: Run a full eigendecomposition on this 4×4 symmetric matrix [[4,2,0,0],[2,3,1,0],[0,1,2,1],[0,0,1,5]] — I need the eigenvalues, eigenvectors, the inertia counts, and both residuals showing how accurate the decomposition is.

## When to prefer this

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.

## Known failure modes

- 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

## 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.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "$schema": "https://json-schema.org/draft/2020-12/schema",
 "required": [
  "input"
 ],
 "properties": {
  "input": {
   "type": "object",
   "required": [
    "type",
    "method",
    "bodyType"
   ],
   "properties": {
    "type": {
     "const": "http"
    },
    "method": {
     "const": "POST"
    },
    "bodyType": {
     "const": "json"
    },
    "schemaUrl": {
     "type": "string",
     "format": "uri"
    },
    "exampleUrl": {
     "type": "string",
     "format": "uri"
    }
   },
   "additionalProperties": true
  },
  "output": {
   "type": "object",
   "required": [
    "type"
   ],
   "properties": {
    "type": {
     "const": "json"
    },
    "schemaUrl": {
     "type": "string",
     "format": "uri"
    },
    "exampleUrl": {
     "type": "string",
     "format": "uri"
    }
   },
   "additionalProperties": true
  }
 },
 "additionalProperties": true
}
```

## More

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