{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.matrix","code":"thing-q44337","url":"https://ver.cy/models/thing/q44337/","name":"matrix","alternateNames":["sparse matrix","dense matrix","complex conjugate matrix","payoff matrix","transformation matrix","generator matrix","risk matrix","co-occurrence matrix","Cauchy matrix","fundamental matrix","Next-generation matrix","Manin matrix"],"kind":"thing","status":"published","version":"0.2.0-wave.2","language":"en","classifiers":{"family":"Thing Registry","category":"Information and virtual systems","entryKind":"thing","plane":"INF","domain":["INF.MED"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"A rectangular array of numbers, symbols or expressions arranged in rows and columns, used to represent linear transformations, systems of equations, graphs, games and data, with operations such as addition, multiplication, transposition and inversion; matrices include special types such as sparse, transformation, payoff and generator matrices and can be represented in computing using array data structures, sparse formats or other representations.","purpose":"Let an agent explain matrices and their operations, perform and check matrix computations, apply matrices in science, engineering and computing, and separate other senses of matrix.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Rectangular array","Defined operations","Represents linear maps","Central to computation"],"structure":{"bundles":[{"id":"compute","name":"Compute","description":"Operations.","layers":[{"id":"operations","name":"Operations","description":"Basic operations.","findings":[{"id":"operations-finding","name":"Operations","description":"Operations.","questions":[{"text":"What is the product, inverse or transpose of these matrices?","kind":"measurement"},{"text":"Are the dimensions compatible?","kind":"boundary"}]}]},{"id":"properties","name":"Properties","description":"Key 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meanings.","questions":[{"text":"Is a biological matrix, a material matrix, a payoff matrix in game theory or the film meant?","kind":"boundary"},{"text":"Which entry fits?","kind":"action"}]}]},{"id":"teach","name":"Teach","description":"Teaching.","findings":[{"id":"teach-finding","name":"Teach","description":"Teaching.","questions":[{"text":"How can matrix operations be taught intuitively?","kind":"action"},{"text":"Which misconceptions arise?","kind":"provenance"}]}]}]}]},"agentConduct":{"may":["Compute with matrices and report results with stated precision.","Explain matrix operations and their uses."],"mustNot":["Present a numerically unstable result as accurate.","Hide errors in matrix computations behind models that affect people's lives, such as credit scoring."],"requiresHuman":["Using matrix-based models for decisions about people."]},"ethics":{"considerations":["Opaque models built on matrices can encode bias in decisions about people.","Mathematics teaching should be accurate and accessible."],"affectedParties":["Students","People affected by models","Engineers relying on computations"]},"owners":{"steward":"Nobody: an abstract concept held in common.","roles":[],"masterSystems":[]},"relations":[{"target":"Q186152","type":"parent","note":"registry parent class"},{"target":"Q188524","type":"parent","note":"registry parent class"},{"target":"array data structure","type":"related","note":"category"},{"target":"tensor","type":"related","note":"category"},{"target":"line segment","type":"related","note":"geometric transformations"},{"target":"probability distribution","type":"related","note":"covariance matrices"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.matrix","Wikidata: Q44337 (https://www.wikidata.org/wiki/Q44337)"]},"properties":{"applicability":"not-applicable","items":[]},"recognition":{"applicability":"optional","items":["Rows and columns","Dimensions m by n","A vector is a single row or column","Not physical; grids of numbers in brackets."]},"capabilities":{"applicability":"required","items":["perform matrix operations","explain properties such as rank, determinant and eigenvalues","apply matrices in transformations and systems","choose storage and algorithms in computing"]},"hazards":{"applicability":"required","items":["Dimension mismatches","Numerical instability","Confusing senses of matrix"]},"interfaces":{"applicability":"required","items":["ISO 80000-2 notation","Numerical library standards such as BLAS and LAPACK"]},"context":{"applicability":"required","items":["Linear algebra, data representation and computation.","square, diagonal and identity matrices","sparse and dense matrices","transformation and rotation matrices","payoff and adjacency matrices","generator and parity-check matrices in coding"]}},"sources":[{"title":"Wikidata item Q44337: matrix","url":"https://www.wikidata.org/wiki/Q44337","note":"identity and sense of the item"},{"title":"Wikipedia: Matrix (mathematics)","url":"https://en.wikipedia.org/wiki/Matrix_%28mathematics%29","note":"general description of the item"}],"openQuestions":["Should each matrix type be a separate entry?","How should numerical libraries be linked?","How should other senses be split?"],"resources":{"spec":"/models/things/publications/thing-q44337/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q44337/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-11T19:32:26Z","builder":"tools/build_cards.py@1.0.0"},"completeness":{"sections":{"classifiers":"filled","whatItIs":"filled","purpose":"filled","distinguishingFeatures":"filled","structure":"filled","agentConduct":"filled","ethics":"filled","owners":"filled","relations":"filled","interaction.identity":"filled","interaction.properties":"not-applicable","interaction.recognition":"filled","interaction.capabilities":"filled","interaction.hazards":"filled","interaction.interfaces":"filled","interaction.context":"filled","sources":"filled"},"notes":{"_gate":"Published through the thing publication gate 1.0 on 2026-10-07T10:10:31+00:00: completeness 1.00; sense: Wikidata description; 2 live sources; review by codex: pass","interaction.properties":"Plane INF: no invented physical properties."},"score":1.0}}