Matrix determinant API

Determinant of a square matrix (closed-form for 2x2/3x3, LU elimination with partial pivoting for NxN), flagging singular matrices. Answers 'what is the determinant?', 'is this matrix invertible?'.

Price$0.02per request

MethodPOST

Route/v1/geometry/matrix-determinant

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

matrixdeterminantsingularinvertiblelinear-algebragaussian

API URLhttps://x402.hexl.dev/v1/geometry/matrix-determinant

Integration docs

Example request

{
  "matrix": [
    [
      6,
      1,
      1
    ],
    [
      4,
      -2,
      5
    ],
    [
      2,
      8,
      7
    ]
  ]
}

Example response

{
  "determinant": -306,
  "size": 3,
  "singular": false,
  "interpretation": "Volume-scaling factor of the transform is 306 (sign flips orientation)."
}

Input schema

{
  "type": "object",
  "required": [
    "matrix"
  ],
  "properties": {
    "matrix": {
      "type": "array",
      "items": {
        "type": "array",
        "items": {
          "type": "number"
        }
      },
      "examples": [
        [
          [
            6,
            1,
            1
          ],
          [
            4,
            -2,
            5
          ],
          [
            2,
            8,
            7
          ]
        ]
      ]
    }
  }
}

Output schema

{
  "type": "object",
  "additionalProperties": true
}