Matrix determinant

matrix-determinant · version 1.0.0 · Vectors & matrices · free, no key needed

Compute the determinant of a small square finite-number matrix.

Use when you need to: matrix determinant · det of a square matrix.

Supported

• matrix determinant
• det of a square matrix

Not supported

• non-square matrices
• matrices larger than 12x12
• symbolic/exact-rational determinant

Behavior

• Input matrix is a square NxN array of finite JSON numbers, N from 1 to 12, magnitude bounded to at most 1000000.
• Computed via Gaussian elimination with partial (largest-magnitude) pivoting in IEEE-754 double precision, accumulating the product of pivots with a sign flip per row swap.
• Results for small integer-valued matrices are typically exact; floating-point rounding can appear for larger, fractional, or ill-conditioned matrices.
• If, at any elimination step, every remaining candidate pivot in a column is exactly 0, the determinant is exactly 0 (the input matrix is singular).
• A result of -0 is normalized to 0.

Input

• matrix (array of array of number, required): min items 1; max items 12

Output

• result (number, required)

Limits

• max dim: 12
• max abs value: 1000000

Example

Request input:

{
  "matrix": [
    [
      1,
      2
    ],
    [
      3,
      4
    ]
  ]
}

Response:

{
  "result": {
    "result": -2
  }
}

How to call it

MCP

Connect https://computefirst.net/mcp (setup), then call execute with:

{
  "id": "matrix-determinant",
  "version": "1.0.0",
  "input": {
    "matrix": [
      [
        1,
        2
      ],
      [
        3,
        4
      ]
    ]
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/matrix-determinant/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"matrix":[[1,2],[3,4]]}'

The machine-readable contract is at /v1/tools/matrix-determinant/versions/1.0.0.

CLI

node cli.mjs run matrix-determinant 1.0.0 --input input.json --base-url https://computefirst.net

Get the client at /clients/cli/.

Related tools

• Matrix inverse: Compute the inverse of a small square finite-number matrix.
• Matrix scale: Multiply every entry of a finite-number matrix by a scalar.
• Matrix trace: Compute the trace (sum of diagonal entries) of a square finite-number matrix.
• Matrix vector multiply: Multiply an MxN finite-number matrix by a length-N finite-number vector, producing a length-M vector.
• Vector outer product: Compute the outer product of two finite-number vectors, producing a matrix.
• Matrix add: Add two equal-shape finite-number matrices elementwise.