# Linear Algebra Eigenvalue & Eigenvector Calculator

> Linear Algebra Eigenvalue & Eigenvector Calculator is a paid API for AI agents from linear-algebra.x402tookit.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-10-29).

Computes eigenvalues and eigenvectors of a 2x2 matrix (closed-form) or a symmetric matrix up to 10x10 (Jacobi iteration), with spectral properties like trace, determinant, and definiteness.

## Facts

- Endpoint: GET https://linear-algebra.x402tookit.com/eigen?utm_source=zero.xyz
- Price: $0.02/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-29
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/linear-algebra-eigenvalue-eigenvector-calculator-1bbf4072
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_se8fmYm2q098Gb_9tna-A

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 linear-algebra-eigenvalue-eigenvector-calculator-1bbf4072
```

Example prompt: What are the eigenvalues and eigenvectors of the symmetric matrix [[4,2,0],[2,3,1],[0,1,5]]? Also tell me if it's positive definite.

## When to prefer this

Choose this endpoint when you need eigenvalues and eigenvectors with full spectral metadata (definiteness, trace, determinant, residual) for a 2x2 matrix or a symmetric matrix up to 10x10. Prefer it over general-purpose CAS tools when you want a lightweight, pay-per-call computation with numerical reliability checks and Jacobi-method accuracy reporting built in.

## Known failure modes

- Non-symmetric matrix larger than 2x2 may be rejected or flagged — only symmetric matrices up to 10x10 are supported beyond 2x2
- Malformed matrix input (non-square, wrong JSON format) returns an error
- Matrix exceeding 10x10 is rejected
- Numerically ill-conditioned or near-defective matrices may return degraded results with a warning flag
- Complex eigenvalues for non-symmetric 2x2 inputs are returned with non-zero imaginary parts

## How this service works

Eigenvalues and eigenvectors of a 2x2 matrix (closed form) or a symmetric matrix up to 10x10 (Jacobi).

## Output

Returns a JSON object containing eigenvalues (as objects with real 're' and imaginary 'im' parts), eigenvectors (as arrays of numbers), trace, determinant, sum and product of eigenvalues, definiteness classification, symmetry flag, the numerical method used (closed-form or Jacobi), max residual error (Av - λv), and any warnings about degraded or defective results.

## 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"
   ],
   "properties": {
    "type": {
     "type": "string",
     "const": "http"
    },
    "method": {
     "enum": [
      "GET"
     ],
     "type": "string"
    },
    "queryParams": {
     "type": "object",
     "required": [
      "A"
     ],
     "properties": {
      "A": {
       "type": "string",
       "description": "2x2 matrix, or symmetric NxN up to 10x10, JSON like [[2,1],[1,2]] or 2,1;1,2"
      }
     }
    }
   },
   "additionalProperties": false
  },
  "output": {
   "type": "object",
   "required": [
    "type"
   ],
   "properties": {
    "type": {
     "type": "string"
    },
    "example": {
     "type": "object",
     "properties": {
      "asOf": {
       "type": [
        "null",
        "string"
       ]
      },
      "size": {
       "type": [
        "null",
        "number"
       ]
      },
      "trace": {
       "type": [
        "null",
        "number"
       ]
      },
      "method": {
       "type": [
        "null",
        "string"
       ]
      },
      "source": {
       "type": [
        "null",
        "string"
       ]
      },
      "reasons": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "string"
       }
      },
      "summary": {
       "type": [
        "null",
        "string"
       ]
      },
      "verdict": {
       "type": [
        "null",
        "string"
       ]
      },
      "degraded": {
       "type": [
        "boolean",
        "null"
       ]
      },
      "defective": {
       "type": [
        "boolean",
        "null"
       ]
      },
      "symmetric": {
       "type": [
        "boolean",
        "null"
       ]
      },
      "disclaimer": {
       "type": [
        "null",
        "string"
       ]
      },
      "notChecked": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "string"
       }
      },
      "determinant": {
       "type": [
        "null",
        "number"
       ]
      },
      "eigenvalues": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "object",
        "properties": {
         "im": {
          "type": [
           "null",
           "number"
          ]
         },
         "re": {
          "type": [
           "
… (truncated)
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/linear-algebra-eigenvalue-eigenvector-calculator-1bbf4072/health.json
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