Matrix rank

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

Compute the numerical rank of a finite-number matrix (square or rectangular).

Use when you need to: matrix rank · row rank · numerical rank.

Supported

• matrix rank
• row rank
• numerical rank

Not supported

• exact symbolic rank over the rationals
• nullspace basis computation

Behavior

• Input matrix is a rectangular MxN array of finite JSON numbers, M and N each from 1 to 20, magnitude bounded to at most 1000000.
• Computed via Gaussian elimination with partial (largest-magnitude) pivoting in IEEE-754 double precision, counting the number of pivot columns found.
• Optional input tolerance (default 1e-9, range 0 to 1) is the minimum pivot magnitude treated as nonzero; smaller candidate pivots are treated as zero for rank purposes.
• The result is an integer between 0 and min(M, N) inclusive.

Input

• matrix (array of array of number, required): min items 1; max items 20
• tolerance (number, optional): min 0; max 1

Output

• result (integer, required)

Limits

• max rows: 20
• max cols: 20
• max abs value: 1000000

Example

Request input:

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

Response:

{
  "result": {
    "result": 1
  }
}

How to call it

MCP

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

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

HTTP (no key)

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

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

CLI

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

Get the client at /clients/cli/.

Related tools

• 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.
• Matrix determinant: Compute the determinant of a small square finite-number matrix.
• Matrix hadamard: Multiply two equal-shape finite-number matrices elementwise (Hadamard product).
• Matrix identity: Construct the NxN identity matrix for a given size.
• Matrix inverse: Compute the inverse of a small square finite-number matrix.