{"uid":"cap_ei3ymwjQN47WWf8LvO6HO","slug":"numora-matrix-lu-decomposition-api-8be30406","name":"Numora Matrix LU Decomposition API","description":"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.","url":"https://numomo.vercel.app/api/matrix/lu","method":"POST","headers":{},"bodySchema":{"type":"object","required":["A"],"properties":{"A":{"type":"array","description":"Matrix (2D array)"}}},"responseSchema":{"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"}}},"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.1","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"registry","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.1/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.1","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.1","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_-JXCzJeuDk-FtKsyfHMYH","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.1","costPer":"request","priority":0,"asset":null,"unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Performs LU decomposition on a square matrix, returning lower and upper triangular factor matrices.","exampleAgentPrompt":"Can you do an LU decomposition on this matrix: [[4, 3], [6, 3]]? I need the lower and upper triangular factors.","exampleUseCases":[{"title":"Solving system of linear equations","prompt":"I have the coefficient matrix [[2, 1, -1], [−3, −1, 2], [−2, 1, 2]] and I need to solve a linear system — can you do an LU decomposition on it so I can use forward and back substitution?"},{"title":"Numerical stability analysis","prompt":"Can you LU-decompose this 3x3 matrix [[10, -7, 0], [-3, 2.099, 6], [5, -1, 5]] so I can check for numerical stability and pivot elements?"},{"title":"Matrix inversion via factorization","prompt":"I need to invert the matrix [[1, 2, 3], [0, 1, 4], [5, 6, 0]] — start by giving me its LU decomposition so I can work through the inversion steps."}],"resultDescription":"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).","failureModes":["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"],"whenToPreferThis":"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.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-16T00:52:01.879Z","isFirstParty":false}