# Numora Matrix LU Decomposition

> Numora Matrix LU Decomposition is a paid API for AI agents from numorapoi.orbonomy.xyz, paid per call via x402, $0.04/call, status unknown (last checked 2026-09-14).

Performs LU decomposition on a 2D matrix, factoring it into lower and upper triangular matrices

## Facts

- Endpoint: POST https://numorapoi.orbonomy.xyz/api/matrix/lu
- Price: $0.04/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-14
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-matrix-lu-decomposition-api-7a9a1e3a
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_Dpj34t3kIcuFbhfsi4d_M

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-7a9a1e3a -d '<json body>'
```

Example prompt: Can you do an LU decomposition on this matrix: [[2, 1, -1], [-3, -1, 2], [-2, 1, 2]]? I need the lower and upper triangular factors.

## When to prefer this

Use this endpoint when you need LU decomposition specifically as a pure math computation with no external dependencies, charged per-call via micropayment. Ideal for agents that need on-demand matrix factorization without setting up a local math library, or when integrating LU factorization into a serverless pipeline.

## Known failure modes

- Non-square matrix provided — returns error if matrix rows and columns don't match
- Singular matrix causes decomposition failure
- Malformed 2D array input (jagged rows, non-numeric values) returns validation error
- Empty matrix or null input returns 400-level error
- Payment failure via x402 micropayment returns 402 status before 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 flag, a computation description string, and a result object containing the L (lower triangular), U (upper triangular), and P (permutation) matrices from the LU factorization of the input matrix.

## 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-7a9a1e3a/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numorapoi.orbonomy.xyz](https://www.zero.xyz/host/numorapoi.orbonomy.xyz/llms.txt)