{"uid":"cap_FAraUNJeyFel6VD8Qu30O","slug":"numora-matrix-null-space-computation-7a2b734c","name":"Numora Matrix Null-Space Computation","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/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_DrgXVtqkK4sGikwwhPc8B","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 given matrix using pure mathematical computation with no external dependencies.","exampleAgentPrompt":"Find the null space of the matrix [[1, 2, 3], [4, 5, 6], [7, 8, 9]] and give me the basis vectors.","exampleUseCases":[{"title":"Solving homogeneous linear systems","prompt":"I have the coefficient matrix [[2, 1, -1], [0, 3, 2], [0, 0, 0]] for a homogeneous system Ax=0 — can you find all the solutions by computing its null space?"},{"title":"Robotics joint-space analysis","prompt":"For my robot arm's Jacobian matrix [[1, 0, -1, 0], [0, 1, 0, -1], [1, 1, 0, 0]], can you compute the null space so I can find the redundant joint motions that produce no end-effector movement?"},{"title":"Dimensionality reduction preprocessing","prompt":"I have this data projection matrix [[1, 2, 2], [2, 4, 4], [3, 6, 6]] — what is its null space so I can identify which input dimensions are linearly redundant?"}],"resultDescription":"Returns a JSON object with 'success' (boolean), 'result' (an object containing the null space basis vectors — the set of all vectors x satisfying Ax=0), and 'computation' (a human-readable string describing what was computed, e.g. the dimensionality of the kernel and the basis found).","failureModes":["Non-2D array provided for matrix A — returns error or unexpected result","Empty matrix or matrix with inconsistent row lengths causes parse failure","Full-rank square matrix returns an empty null space (trivial kernel), which is valid but may surprise users expecting non-trivial results","Very large matrices may time out or exceed computation limits","Non-numeric values in matrix cells cause computation failure"],"whenToPreferThis":"Choose this endpoint when you need the exact mathematical null space (kernel) of a matrix in a pure, dependency-free computation context, especially when paying per-call via x402 micropayments is acceptable and you want a lightweight hosted math service rather than running a local linear algebra library. Prefer it over general-purpose code execution environments when you want a simple POST-and-get-result interface for null space specifically.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-15T18:48:33.017Z","isFirstParty":false}