# Linear Algebra Determinant Calculator

> Linear Algebra Determinant 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 the determinant of a square matrix (up to 10x10) using LU decomposition with partial pivoting, with numerical singularity detection.

## Facts

- Endpoint: GET https://linear-algebra.x402tookit.com/determinant?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-determinant-calculator-7d9ece12
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_GIQdMPBaXdHE6H2TFnq_Q

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-determinant-calculator-7d9ece12
```

Example prompt: Can you compute the determinant of the matrix [[2,3,1],[4,5,6],[7,8,9]] and tell me if it's singular?

## When to prefer this

Use this endpoint when you need a fast, numerically stable determinant calculation for matrices up to 10x10, especially when you also need to detect near-singularity. Prefer this over general-purpose math libraries when you want a hosted, pay-per-use solution with no setup, or when building an agent pipeline that needs singularity checks before attempting inversion or solving a linear system.

## Known failure modes

- Non-square matrix input returns an error
- Matrix larger than 10x10 is rejected
- Malformed JSON or invalid delimiter format causes a parse error
- Numerically near-singular matrix may return singular:true with a near-zero determinant
- Missing required query parameter A returns a validation error

## How this service works

Determinant of a square matrix (up to 10x10) by LU with partial pivoting, flagging a numerically singular matrix.

## Output

Returns the numerical determinant value, a boolean singular flag (true if numerically singular), the matrix size, and a ratio of the determinant relative to the Hadamard bound. Also includes source and timestamp metadata.

## 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": "Square matrix, JSON like [[1,2],[3,4]] or 1,2;3,4 (max 10x10)"
      }
     }
    }
   },
   "additionalProperties": false
  },
  "output": {
   "type": "object",
   "required": [
    "type"
   ],
   "properties": {
    "type": {
     "type": "string"
    },
    "example": {
     "type": "object",
     "properties": {
      "asOf": {
       "type": [
        "null",
        "string"
       ]
      },
      "size": {
       "type": [
        "null",
        "number"
       ]
      },
      "source": {
       "type": [
        "null",
        "string"
       ]
      },
      "reasons": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "string"
       }
      },
      "summary": {
       "type": [
        "null",
        "string"
       ]
      },
      "verdict": {
       "type": [
        "null",
        "string"
       ]
      },
      "degraded": {
       "type": [
        "boolean",
        "null"
       ]
      },
      "singular": {
       "type": [
        "boolean",
        "null"
       ]
      },
      "disclaimer": {
       "type": [
        "null",
        "string"
       ]
      },
      "notChecked": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "string"
       }
      },
      "determinant": {
       "type": [
        "null",
        "number"
       ]
      },
      "relativeToHadamardBound": {
       "type": [
        "null",
        "number"
       ]
      }
     }
    }
   }
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/linear-algebra-determinant-calculator-7d9ece12/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from linear-algebra.x402tookit.com](https://www.zero.xyz/host/linear-algebra.x402tookit.com/llms.txt)