{"uid":"cap_fNryQZQSVmyT6kYH_NrLb","slug":"numora-matrix-null-space-12ac9d1d","name":"Numora Matrix Null Space","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/null-space","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_NrAYkfJCdueBkzNxH3vFf","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 null space (kernel) of a matrix — the set of all vectors x such that Ax = 0","exampleAgentPrompt":"Find the null space of this matrix: [[1, 2, 3], [4, 5, 6], [7, 8, 9]] — I need the basis vectors for all solutions to Ax=0.","exampleUseCases":[{"title":"Solving underdetermined linear systems","prompt":"I have a system of equations represented by the matrix [[1, 2, -1, 0], [2, 4, -2, 0], [0, 1, 1, -1]] and I need to find all vectors in its null space so I can characterize the full solution set."},{"title":"Checking linear dependence of columns","prompt":"Can you compute the null space of [[1, 2, 3], [4, 5, 6], [7, 8, 9]] to figure out whether there are non-trivial dependencies among the columns of this matrix?"},{"title":"Finding degrees of freedom in a constraint system","prompt":"I'm working on a robotics constraint matrix [[1, 0, -1, 2], [0, 1, 1, -1]] and I need the null space to determine how many degrees of freedom the system has."}],"resultDescription":"Returns a JSON object with a 'success' boolean, a 'result' object containing the null space basis vectors (spanning vectors of the kernel), and a human-readable 'computation' string describing what was calculated. If the null space is trivial (only the zero vector), the result will indicate that.","failureModes":["Non-rectangular or malformed 2D array input returns an error","Matrix with non-numeric entries will fail","Missing required 'A' field returns validation error","Extremely large matrices may time out or exceed memory limits","Singular or near-singular matrices handled numerically — may have floating-point precision issues"],"whenToPreferThis":"Use this endpoint when you need pure mathematical computation of a matrix null space with no external dependencies, billed per-call via x402 micropayments. Prefer this over symbolic math libraries when you want a lightweight, serverless, pay-per-use solution with a simple REST interface. Best suited for AI agents needing on-demand linear algebra within automated pipelines.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-14T12:49:57.518Z","isFirstParty":false}