{"uid":"cap_QU48CenpD1h9OdNvZho2p","slug":"matrix-determinant-calculator-07066ec1","name":"Matrix Determinant Calculator","description":"Compute the determinant of a square matrix via Gaussian elimination with partial pivoting. A non-square, ragged or empty matrix is a clean 400; a singular matrix simply returns 0.","url":"https://matrix.openverbs.com/v1/determinant","method":"POST","headers":{},"bodySchema":{"type":"object","$schema":"https://json-schema.org/draft/2020-12/schema","required":["input"],"properties":{"input":{"type":"object","required":["type","method","bodyType","body"],"properties":{"body":{"type":"object","required":["matrix"],"properties":{"matrix":{"type":"array","items":{"type":"array","items":{"type":"number"},"minItems":1},"minItems":1,"description":"Square matrix (n×n)."}},"additionalProperties":false},"type":{"type":"string","const":"http"},"method":{"enum":["POST"],"type":"string"},"bodyType":{"enum":["json","form-data","text"],"type":"string"}},"additionalProperties":false}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.004","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","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":"$0.004/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.004","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.004","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_RWUf0fPy5E4PsAHaNOBKX","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.004","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes the determinant of a square matrix using Gaussian elimination with partial pivoting","exampleAgentPrompt":"What's the determinant of the matrix [[3, 8], [4, 6]]?","exampleUseCases":[{"title":"Check matrix invertibility before solving system","prompt":"Before I try to solve this linear system, can you check if the coefficient matrix [[2, 1, -1], [−3, −1, 2], [−2, 1, 2]] is invertible by computing its determinant?"},{"title":"Compute determinant for eigenvalue analysis","prompt":"I need the determinant of the 4×4 matrix [[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16]] as part of finding its eigenvalues — can you calculate that?"},{"title":"Validate singular matrix in data pipeline","prompt":"Our data pipeline needs to flag degenerate cases — can you compute the determinant of this matrix [[1,2,3],[4,5,6],[7,8,9]] so I can check if it's singular?"}],"resultDescription":"Returns a single numeric scalar representing the determinant of the input matrix. For a singular matrix (det = 0), returns 0. For non-square, ragged, or empty matrices, returns a 400 error.","failureModes":["Non-square matrix submitted: returns 400 with clean error","Ragged matrix (rows of unequal length): returns 400","Empty matrix (zero rows or zero columns): returns 400","Singular matrix: returns 0 (not an error, by design)","Malformed JSON body or missing matrix field: returns 400"],"whenToPreferThis":"Choose this endpoint when you need a fast, reliable scalar determinant for a square numeric matrix — especially in automated pipelines requiring invertibility checks, condition analysis, or pre-validation before matrix inversion or linear system solving. It handles singular matrices gracefully (returns 0 rather than erroring), making it safe for batch use. Prefer this over general-purpose math libraries when you need a pay-per-call API that integrates easily into agentic workflows.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-14T12:34:21.850Z","isFirstParty":false}