# Saylor Innovations Matrix Calculator

> Saylor Innovations Matrix Calculator is a paid API for AI agents from saylorinnovations.com, paid per call via x402, $0.01/call, status unknown (last checked 2026-10-18).

Computes determinant, inverse, rank, trace, transpose, and solves linear systems Ax=b for matrices up to 8x8

## Facts

- Endpoint: GET https://saylorinnovations.com/api/math/matrix?utm_source=zero.xyz
- Price: $0.01/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-18
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/saylor-innovations-matrix-calculator-37f217cb
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_paeqGBEp1Q-SjTVgMkr1O

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 saylor-innovations-matrix-calculator-37f217cb
```

Example prompt: Can you compute the determinant, inverse, rank, and trace of the matrix [[2,1,0],[1,3,1],[0,1,2]], and also solve for x in Ax=b where b is [1,2,3]?

## When to prefer this

Choose this endpoint when you need quick, accurate linear algebra computations on matrices up to 8x8, especially when you need multiple properties (determinant, inverse, rank, trace, transpose) in a single call or need to solve a linear system Ax=b. It's ideal for educational tools, engineering calculations, or any workflow requiring symbolic or numerical matrix analysis without standing up a local math library.

## Known failure modes

- Matrix larger than 8x8 rejected
- Malformed JSON array in matrix parameter causes error
- Non-numeric values in matrix cause computation failure
- Solving Ax=b with a singular (non-invertible) matrix returns null solution
- Missing required matrix parameter returns error
- Providing vector b with a non-square matrix may return null solution

## How this service works

Matrix calculator for up to 8x8 - determinant, inverse, rank, trace, transpose and the solution of the linear system Ax = b with a square matrix

## Output

A JSON object containing: number of rows and columns, whether the matrix is square, its rank, trace (null for non-square), determinant (null for non-square), whether it is invertible, the inverse matrix (null if not invertible), the transposed matrix, and the solution vector x for Ax=b if a vector b was provided.

## 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": [
      "matrix"
     ],
     "properties": {
      "b": {
       "type": "string",
       "description": "optional right-hand side vector to solve Ax = b"
      },
      "matrix": {
       "type": "string",
       "description": "JSON array of rows, up to 8x8, e.g. [[1,2],[3,4]]"
      }
     }
    }
   },
   "additionalProperties": false
  },
  "output": {
   "type": "object",
   "required": [
    "type"
   ],
   "properties": {
    "type": {
     "type": "string",
     "const": "json"
    },
    "example": {
     "type": "object",
     "required": [
      "rows",
      "cols",
      "rank"
     ],
     "properties": {
      "cols": {
       "type": "number",
       "description": "Number of columns"
      },
      "rank": {
       "type": "number",
       "description": "Rank, 1 is highest"
      },
      "rows": {
       "type": "number",
       "description": "List of rows"
      },
      "trace": {
       "type": [
        "number",
        "null"
       ],
       "description": "Sum of the diagonal, null for non-square matrices"
      },
      "source": {
       "type": "string",
       "description": "Data source the values come from"
      },
      "square": {
       "type": "boolean",
       "description": "True when the matrix is square"
      },
      "inverse": {
       "type": [
        "array",
        "null"
       ],
       "description": "Inverse matrix, or null"
      },
      "solution": {
       "type": [
        "array",
        "null"
       ],
       "description": "Solution vector of Ax = b, or null"
      },
      "transpose": {
       "type": "array",
       "description": "Transposed matrix"
      },
      "invertible": {
       "type": [
        "boolean",
        "null"
       ],
       "description": "True when the matrix has an inverse"
      },
      "determinant": {
       "type": [
        "number",
        "null"
       ],
       "description": "Determinant, null for non-square matrices"
      }
     }
    }
   }
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/saylor-innovations-matrix-calculator-37f217cb/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from saylorinnovations.com](https://www.zero.xyz/host/saylorinnovations.com/llms.txt)