{"uid":"cap_UQY-tR7jEGI14gs2o2Tof","slug":"numora-qr-decomposition-api-f8ef025c","name":"Numora QR 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/qr","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_M6YxDbyRxYNt5WQgwVoSz","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":"Computes the QR decomposition of a matrix, returning orthogonal (Q) and upper-triangular (R) factor matrices","exampleAgentPrompt":"Can you do a QR decomposition of this matrix: [[12, -51, 4], [6, 167, -68], [-4, 24, -41]]?","exampleUseCases":[{"title":"Least squares regression fitting","prompt":"I have an overdetermined system I need to solve — can you QR-decompose this coefficient matrix [[1,1],[1,2],[1,3],[1,4]] so I can use it for least squares fitting?"},{"title":"Orthogonalization of basis vectors","prompt":"I need to orthogonalize these basis vectors using QR decomposition — the matrix is [[3,1],[4,1],[5,9],[2,6]]. Can you factor it into Q and R?"},{"title":"Numerical stability check for matrix","prompt":"Can you QR-decompose my 3x3 matrix [[2,1,0],[1,3,1],[0,1,2]] so I can inspect the R factor for near-zero diagonal entries that would indicate rank deficiency?"}],"resultDescription":"Returns a JSON object with success=true, a result object containing the Q (orthogonal) and R (upper-triangular) factor matrices, and a human-readable computation description string explaining what was computed.","failureModes":["Non-rectangular or malformed 2D array returns an error","Empty matrix input causes failure","Non-numeric values in matrix entries cause computation error","Singular or rank-deficient matrices may produce degenerate results","Missing required field A returns a 400-level error"],"whenToPreferThis":"Choose this endpoint when you need a pure, dependency-free QR matrix factorization without setting up a local numerical library. Ideal for AI agents performing on-the-fly linear algebra as part of a larger workflow — e.g. solving least squares problems, orthogonalizing basis sets, or preprocessing matrices for eigenvalue computations — where spinning up Python/numpy is not viable. Priced per-call at $0.1 USDC via x402 micropayments on Base, suitable for occasional agent use rather than high-volume batch jobs.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-15T18:55:54.109Z","isFirstParty":false}