# Numora LU Decomposition API

> Numora LU Decomposition API is a paid API for AI agents from numormo.vercel.app, paid per call via x402, $0.1/call, status unknown (last checked 2026-09-14).

Performs LU decomposition on a matrix, factoring it into lower and upper triangular matrices for use in solving linear systems and related computations

## Facts

- Endpoint: POST https://numormo.vercel.app/api/matrix/lu
- Price: $0.1/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-14
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-lu-decomposition-api-f878bfe2
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_CBkHb5F53L-X60SHm1rN0

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-lu-decomposition-api-f878bfe2 -d '<json body>'
```

Example prompt: Can you perform 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 in an agent workflow without spinning up a numerical computing environment. Ideal for scenarios requiring repeated solves of Ax=b with different right-hand sides, inverting matrices, or computing determinants as intermediate steps. Prefer this over general-purpose compute endpoints when you need a lightweight, pay-per-call math API on Base with no setup overhead.

## Known failure modes

- Non-square matrix provided — returns error since LU decomposition requires a square matrix
- Singular or near-singular matrix — may fail or return degenerate factors
- Malformed input (non-numeric values, jagged arrays) — returns validation error
- Empty matrix array — returns missing or invalid input error
- Payment failure via x402 — request not processed if USDC micropayment on Base is not completed

## 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=true, a human-readable computation description, and a result object containing the L (lower triangular) and U (upper triangular) matrices from the LU factorization, along with any permutation information used during partial pivoting.

## 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-lu-decomposition-api-f878bfe2/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numormo.vercel.app](https://www.zero.xyz/host/numormo.vercel.app/llms.txt)