# Matrix multiply

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

Multiply an MxK finite-number matrix by a KxN finite-number matrix, producing an MxN matrix.

**Use when you need to: matrix multiplication · matrix product · multiply two matrices.**

## Supported

- matrix multiplication
- matrix product
- multiply two matrices

## Not supported

- elementwise multiplication (use matrix-hadamard)
- incompatible inner dimensions
- sparse matrix representation

## Behavior

- Input a is an MxK matrix and b is a KxN matrix of finite JSON numbers; a columns must equal b rows. M, K, N are each from 1 to 20.
- Each entry magnitude is bounded to at most 1000000 before multiplication.
- The result is the standard MxN matrix product, result[r][c] = sum over k of a[r][k] * b[k][c], accumulated left-to-right in IEEE-754 double precision.
- A result entry of -0 is normalized to 0.

## Input

- `a` (array of array of number, required): min items 1; max items 20
- `b` (array of array of number, required): min items 1; max items 20

## Output

- `result` (array of array of number, required)

## Limits

- max dim: 20
- max abs value: 1000000

## Example

Request input:

```json
{
  "a": [
    [
      1,
      2
    ],
    [
      3,
      4
    ]
  ],
  "b": [
    [
      5,
      6
    ],
    [
      7,
      8
    ]
  ]
}
```

Response:

```json
{
  "result": {
    "result": [
      [
        19,
        22
      ],
      [
        43,
        50
      ]
    ]
  }
}
```

## How to call it

### MCP

Connect `https://computefirst.net/mcp` ([setup](/docs#connect)), then call `execute` with:

```json
{
  "id": "matrix-multiply",
  "version": "1.0.0",
  "input": {
    "a": [
      [
        1,
        2
      ],
      [
        3,
        4
      ]
    ],
    "b": [
      [
        5,
        6
      ],
      [
        7,
        8
      ]
    ]
  }
}
```

### HTTP (no key)

```sh
curl -X POST https://computefirst.net/v1/tools/matrix-multiply/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"a":[[1,2],[3,4]],"b":[[5,6],[7,8]]}'
```

The machine-readable contract is at [/v1/tools/matrix-multiply/versions/1.0.0](/v1/tools/matrix-multiply/versions/1.0.0).

### CLI

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

Get the client at [/clients/cli/](/clients/cli/).

## Related tools

- [Matrix hadamard](/tools/matrix-hadamard): Multiply two equal-shape finite-number matrices elementwise (Hadamard product).
- [Matrix vector multiply](/tools/matrix-vector-multiply): Multiply an MxN finite-number matrix by a length-N finite-number vector, producing a length-M vector.
- [Vector outer product](/tools/vector-outer-product): Compute the outer product of two finite-number vectors, producing a matrix.
- [Matrix scale](/tools/matrix-scale): Multiply every entry of a finite-number matrix by a scalar.
- [Vector dot](/tools/vector-dot): Compute the dot (scalar) product of two equal-length finite-number vectors.
- [Vector hadamard](/tools/vector-hadamard): Multiply two equal-length finite-number vectors elementwise (Hadamard product).