{
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    "publishableCanonical": false,
    "generatedAt": "2026-09-11T19:32:26Z",
    "providers": [
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    "breadth": "written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify",
    "pass": 2,
    "wave": 2,
    "engine": "claude",
    "enrichment": {
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      "engine": "claude",
      "producedAt": "2026-10-05T18:30:00Z",
      "ingestedAt": "2026-10-05T13:35:26+00:00",
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        "owners"
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      "INF.MED"
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    "name": "matrix",
    "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.",
    "definition": "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.",
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      "explain properties such as rank, determinant and eigenvalues",
      "apply matrices in transformations and systems",
      "choose storage and algorithms in computing"
    ],
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      "Defined operations",
      "Represents linear maps",
      "Central to computation"
    ],
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    "visual_identification": [
      "Rows and columns",
      "Dimensions m by n",
      "A vector is a single row or column"
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    "physical_properties": [],
    "families_and_kinds": [
      "square, diagonal and identity matrices",
      "sparse and dense matrices",
      "transformation and rotation matrices",
      "payoff and adjacency matrices",
      "generator and parity-check matrices in coding"
    ],
    "related_models": [
      {
        "relation": "is a kind of",
        "target": "array data structure",
        "why": "category"
      },
      {
        "relation": "is a kind of",
        "target": "tensor",
        "why": "category"
      },
      {
        "relation": "is related to",
        "target": "line segment",
        "why": "geometric transformations"
      },
      {
        "relation": "is related to",
        "target": "probability distribution",
        "why": "covariance matrices"
      }
    ],
    "identifiers": [],
    "standards_and_regulation": [
      "ISO 80000-2 notation",
      "Numerical library standards such as BLAS and LAPACK"
    ],
    "failure_modes_and_hazards": [
      "Dimension mismatches",
      "Numerical instability",
      "Confusing senses of matrix"
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "Compute with matrices and report results with stated precision.",
        "Explain matrix operations and their uses."
      ],
      "must_not": [
        "Present a numerically unstable result as accurate.",
        "Hide errors in matrix computations behind models that affect people's lives, such as credit scoring."
      ],
      "requires_human": [
        "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."
      ],
      "affected_parties": [
        "Students",
        "People affected by models",
        "Engineers relying on computations"
      ]
    },
    "owners": {
      "steward": "Nobody: an abstract concept held in common.",
      "master_systems": []
    }
  },
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      "id": "wikidata",
      "title": "Wikidata item Q44337: matrix",
      "url": "https://www.wikidata.org/wiki/Q44337",
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  ],
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        "name": "Compute",
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        "rationale": "Rules of algebra.",
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          {
            "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 properties.",
            "findings": [
              {
                "id": "properties-finding",
                "name": "Properties",
                "description": "Properties.",
                "questions": [
                  {
                    "text": "What are the rank, determinant and eigenvalues of this matrix?",
                    "kind": "measurement"
                  },
                  {
                    "text": "What do they tell about the linear map?",
                    "kind": "definition"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "apply",
        "name": "Apply",
        "description": "Applications.",
        "rationale": "Matrices everywhere.",
        "layers": [
          {
            "id": "transform",
            "name": "Transform",
            "description": "Transformations.",
            "findings": [
              {
                "id": "transform-finding",
                "name": "Transform",
                "description": "Transformations.",
                "questions": [
                  {
                    "text": "Which matrix represents this rotation, scaling or projection?",
                    "kind": "definition"
                  },
                  {
                    "text": "How are transformations composed?",
                    "kind": "definition"
                  }
                ]
              }
            ]
          },
          {
            "id": "systems",
            "name": "Systems",
            "description": "Linear systems.",
            "findings": [
              {
                "id": "systems-finding",
                "name": "Systems",
                "description": "Linear systems.",
                "questions": [
                  {
                    "text": "How is this system of equations solved with matrices?",
                    "kind": "action"
                  },
                  {
                    "text": "Is the system well-conditioned?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "computing",
        "name": "Computing",
        "description": "Storage and algorithms.",
        "rationale": "Efficiency matters.",
        "layers": [
          {
            "id": "storage",
            "name": "Storage",
            "description": "Sparse and dense.",
            "findings": [
              {
                "id": "storage-finding",
                "name": "Storage",
                "description": "Storage.",
                "questions": [
                  {
                    "text": "Should this matrix be stored as sparse or dense, and in which format?",
                    "kind": "action"
                  },
                  {
                    "text": "How large is it?",
                    "kind": "measurement"
                  }
                ]
              }
            ]
          },
          {
            "id": "numerics",
            "name": "Numerics",
            "description": "Numerical stability.",
            "findings": [
              {
                "id": "numerics-finding",
                "name": "Numerics",
                "description": "Numerics.",
                "questions": [
                  {
                    "text": "Which algorithm and library should be used for this computation?",
                    "kind": "action"
                  },
                  {
                    "text": "How can numerical error be controlled?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "senses",
        "name": "Senses",
        "description": "Disambiguation.",
        "rationale": "Matrix has other senses.",
        "layers": [
          {
            "id": "other",
            "name": "Other",
            "description": "Other meanings.",
            "findings": [
              {
                "id": "other-finding",
                "name": "Other",
                "description": "Other 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"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Should each matrix type be a separate entry?",
    "How should numerical libraries be linked?",
    "How should other senses be split?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}