{"uid":"cap_CBkHb5F53L-X60SHm1rN0","slug":"numora-lu-decomposition-api-f878bfe2","name":"Numora 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://numormo.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_B7nkUpAliu3nXn2alFPhs","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 matrix, factoring it into lower and upper triangular matrices for use in solving linear systems and related computations","exampleAgentPrompt":"Can you perform LU decomposition on this matrix: [[4, 3], [6, 3]]? I need the lower and upper triangular factors.","exampleUseCases":[{"title":"Solving a system of linear equations","prompt":"I need to solve a system of linear equations. Can you do LU decomposition on this coefficient matrix [[2, 1, -1], [-3, -1, 2], [-2, 1, 2]] so I can use the L and U factors to find the solution?"},{"title":"Engineering stiffness matrix factorization","prompt":"I have this stiffness matrix [[10, -2, 0], [-2, 8, -1], [0, -1, 5]] from a structural analysis problem — can you run LU decomposition on it so I can efficiently solve multiple load cases?"},{"title":"Validating numerical stability of a matrix","prompt":"Can you LU-decompose this matrix [[1, 2, 3], [4, 5, 6], [7, 8, 10]] for me? I want to inspect the U factor to check if it's numerically well-conditioned before I use it in further calculations."}],"resultDescription":"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.","failureModes":["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"],"whenToPreferThis":"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.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-14T19:06:55.056Z","isFirstParty":false}