# Numora Matrix LU Decomposition API

> Numora Matrix LU Decomposition API is a paid API for AI agents from numomo.vercel.app, paid per call via x402, $0.1/call, status unknown (last checked 2026-09-16).

Performs LU decomposition on a square matrix, returning lower and upper triangular factor matrices.

## Facts

- Endpoint: POST https://numomo.vercel.app/api/matrix/lu
- Price: $0.1/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-16
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-matrix-lu-decomposition-api-8be30406
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_ei3ymwjQN47WWf8LvO6HO

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 numora-matrix-lu-decomposition-api-8be30406 -d '<json body>'
```

Example prompt: Can you do an LU decomposition on this matrix: [[4, 3], [6, 3]]? I need the lower and upper triangular factors.

## When to prefer this

Choose this endpoint when you need pure, dependency-free LU matrix factorization as a computation primitive — ideal for agents doing linear algebra pipelines, equation solving, or numerical methods without spinning up a Python/NumPy environment. Best when you want a fast, pay-per-call API with no server setup, especially in agentic workflows where math computation is a discrete step.

## Known failure modes

- Non-square matrix input causes an error — LU decomposition requires square matrices
- Singular or near-singular matrix may cause numerical failure or infinite values
- Malformed 2D array (ragged rows, non-numeric values) returns a validation error
- Empty matrix or null input returns a 400-level error
- Payment failure via x402 micropayment protocol prevents computation

## How this service works

100 pure math computation endpoints for AI agents. Statistics, financial math, linear algebra, equation solving, calculus, number theory, sequence generation, and unit conversions. Zero external dependencies. x402 micropayments on Base.

## Output

Returns a JSON object with 'success' (boolean), 'computation' (human-readable description of the LU decomposition performed), and 'result' (object containing the L lower-triangular matrix, U upper-triangular matrix, and optionally a permutation matrix P or pivot indices).

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "A"
 ],
 "properties": {
  "A": {
   "type": "array",
   "description": "Matrix (2D array)"
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "success",
  "result",
  "computation"
 ],
 "properties": {
  "result": {
   "type": "object",
   "description": "Computation result varies by endpoint"
  },
  "success": {
   "type": "boolean",
   "description": "Always true on success"
  },
  "computation": {
   "type": "string",
   "description": "Human-readable description of what was computed"
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/numora-matrix-lu-decomposition-api-8be30406/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numomo.vercel.app](https://www.zero.xyz/host/numomo.vercel.app/llms.txt)