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cross product

Relationships observed in Wikidata. Connections do not establish verification or source support.

Release: sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7

Provider: Wikidata · graph projection only.

OBSERVED · GRAPH-PROJECTION · NOT ADMITTED · NOT VERIFIED · NOT SUPPORT

Edge identity is the provider property id (for example P31). It is not a Counterpedia predicate.

Development requests are not available on this deployment. The observed entity and its graph links remain readable.

Relationships of cross product

Show relationship types (drawing only; the text lists are unaffected)
different from (Observed provider relationships)subclass of (Observed provider relationships)Relationship label not yet available (Observed provider relationships)Relationship label not yet available (Observed provider relationships)Relationship label not yet available (Observed provider relationships)Relationship label not yet available (Observed provider relationships)Relationship label not yet available (Observed provider relationships)Relationship label not yet available (Observed provider relationships)Relationship label not yet available (Observed provider relationships)Relationship label not yet available (Observed provider relationships)Relationship label not yet available (Observed provider relationships)Relationship label not yet available (Observed provider relationships)described by source (Observed provider relationships)Relationship label not yet available (Observed provider relationships)Commons category (Observed provider relationships)subclass of (Observed provider relationships)Relationship label not yet available (Observed provider relationships)Relationship label not yet available (Observed provider relationships)different from (Observed provider relationships)Relationship label not yet available (Observed provider relationships)cross product — Wikidata entity (Q178192)cross productWIKIDATA ENTITYvector multiplication — Wikidata entity (Q56457918)vectormultiplicationWIKIDATA ENTITY\boldsymbol{a} — Literal value (wikidata:literal:2:\boldsymbol{a})\boldsymbol{a}LITERAL VALUE\varepsilon_{i j k} — Literal value (wikidata:literal:3:\varepsilon_{i j k})\varepsilon_{i jk}LITERAL VALUEanticommutativity — Wikidata entity (Q639608)anticommutativityWIKIDATA ENTITY× — Wikidata entity (Q1900125)×WIKIDATA ENTITYWikipedia:Vital articles/Level/4 — Wikidata entity (Q6173448)Wikipedia:Vitalarticles/Level/4WIKIDATA ENTITY\boldsymbol{b} — Literal value (wikidata:literal:7:\boldsymbol{b})\boldsymbol{b}LITERAL VALUEWikiProject Mathematics — Wikidata entity (Q8487137)WikiProjectMathematicsWIKIDATA ENTITY— — Literal value (wikidata:literal:9:—)—LITERAL VALUE\boldsymbol{a} \times \boldsymbol{b} = \begin{pmatrix} a_y b_z - a_z b_y \\ a_z b_x - a_x b_z \\ a_x b_y - a_y b_x \end{pmatrix} — Literal value (wikidata:literal:10:\boldsymbol{a} \times \boldsymbol{b} = \begin{pmatrix} a_y b_z - a_z b_y \\ a_z b_x - a_x b_z \\ a_x b_y - a_y b_x \end{pmatrix})\boldsymbol{a}\times…LITERAL VALUEa_i — Literal value (wikidata:literal:11:a_i)a_iLITERAL VALUEISO 80000-2:2019 Quantities and units — Part 2: Mathematics — Wikidata entity (Q109490582)ISO 80000-2:2019Quantities and…WIKIDATA ENTITY\boldsymbol{a} \times \boldsymbol{b} — Literal value (wikidata:literal:13:\boldsymbol{a} \times \boldsymbol{b})\boldsymbol{a}\times…LITERAL VALUECross product — Literal value (wikidata:literal:14:Cross product)Cross productLITERAL VALUEbinary operation — Wikidata entity (Q164307)binary operationWIKIDATA ENTITY(\boldsymbol{a} \times \boldsymbol{b})_i = \sum_j \sum_k \varepsilon_{i j k} a_j b_k — Literal value (wikidata:literal:16:(\boldsymbol{a} \times \boldsymbol{b})_i = \sum_j \sum_k \varepsilon_{i j k} a_j b_k)(\boldsymbol{a}\times…LITERAL VALUEb_i — Literal value (wikidata:literal:17:b_i)b_iLITERAL VALUEsquare brackets — Wikidata entity (Q2751137)square bracketsWIKIDATA ENTITY

Legend

  • Governed record relationships (solid)
  • Countergraph traversal (dashed)
  • Countergraph evidence (dotted)
  • Observed provider relationships (dash-dot)
  • Structurally derived (sparse dots)

Node shape identifies node kind only. Size, color, and position carry no meaning beyond hop distance from the root.

A line means a supported artifact carried an explicit structured relation. It does not mean the relation is true, admitted, verified, or authoritative.

Graph as text

Nodes (19)

  • cross product — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q178192
    stable_ref
    Q178192
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q178192
    provider
    wikidata
    entity_href
    /entries/wikidata/Q178192
  • vector multiplication — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q56457918
    stable_ref
    Q56457918
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q56457918
    provider
    wikidata
    entity_href
    /entries/wikidata/Q56457918
  • \boldsymbol{a} — Literal value
    Technical details
    node_id
    wikidata:literal:2:\boldsymbol{a}
    stable_ref
    wikidata:literal:2:\boldsymbol{a}
    node_kind
    wikidata_literal
    plane
    provider_observed
  • \varepsilon_{i j k} — Literal value
    Technical details
    node_id
    wikidata:literal:3:\varepsilon_{i j k}
    stable_ref
    wikidata:literal:3:\varepsilon_{i j k}
    node_kind
    wikidata_literal
    plane
    provider_observed
  • anticommutativity — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q639608
    stable_ref
    Q639608
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q639608
    provider
    wikidata
    entity_href
    /entries/wikidata/Q639608
  • × — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q1900125
    stable_ref
    Q1900125
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q1900125
    provider
    wikidata
    entity_href
    /entries/wikidata/Q1900125
  • Wikipedia:Vital articles/Level/4 — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q6173448
    stable_ref
    Q6173448
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q6173448
    provider
    wikidata
    entity_href
    /entries/wikidata/Q6173448
  • \boldsymbol{b} — Literal value
    Technical details
    node_id
    wikidata:literal:7:\boldsymbol{b}
    stable_ref
    wikidata:literal:7:\boldsymbol{b}
    node_kind
    wikidata_literal
    plane
    provider_observed
  • WikiProject Mathematics — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q8487137
    stable_ref
    Q8487137
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q8487137
    provider
    wikidata
    entity_href
    /entries/wikidata/Q8487137
  • — — Literal value
    Technical details
    node_id
    wikidata:literal:9:—
    stable_ref
    wikidata:literal:9:—
    node_kind
    wikidata_literal
    plane
    provider_observed
  • \boldsymbol{a} \times \boldsymbol{b} = \begin{pmatrix} a_y b_z - a_z b_y \\ a_z b_x - a_x b_z \\ a_x b_y - a_y b_x \end{pmatrix} — Literal value
    Technical details
    node_id
    wikidata:literal:10:\boldsymbol{a} \times \boldsymbol{b} = \begin{pmatrix} a_y b_z - a_z b_y \\ a_z b_x - a_x b_z \\ a_x b_y - a_y b_x \end{pmatrix}
    stable_ref
    wikidata:literal:10:\boldsymbol{a} \times \boldsymbol{b} = \begin{pmatrix} a_y b_z - a_z b_y \\ a_z b_x - a_x b_z \\ a_x b_y - a_y b_x \end{pmatrix}
    node_kind
    wikidata_literal
    plane
    provider_observed
  • a_i — Literal value
    Technical details
    node_id
    wikidata:literal:11:a_i
    stable_ref
    wikidata:literal:11:a_i
    node_kind
    wikidata_literal
    plane
    provider_observed
  • ISO 80000-2:2019 Quantities and units — Part 2: Mathematics — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q109490582
    stable_ref
    Q109490582
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q109490582
    provider
    wikidata
    entity_href
    /entries/wikidata/Q109490582
  • \boldsymbol{a} \times \boldsymbol{b} — Literal value
    Technical details
    node_id
    wikidata:literal:13:\boldsymbol{a} \times \boldsymbol{b}
    stable_ref
    wikidata:literal:13:\boldsymbol{a} \times \boldsymbol{b}
    node_kind
    wikidata_literal
    plane
    provider_observed
  • Cross product — Literal value
    Technical details
    node_id
    wikidata:literal:14:Cross product
    stable_ref
    wikidata:literal:14:Cross product
    node_kind
    wikidata_literal
    plane
    provider_observed
  • binary operation — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q164307
    stable_ref
    Q164307
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q164307
    provider
    wikidata
    entity_href
    /entries/wikidata/Q164307
  • (\boldsymbol{a} \times \boldsymbol{b})_i = \sum_j \sum_k \varepsilon_{i j k} a_j b_k — Literal value
    Technical details
    node_id
    wikidata:literal:16:(\boldsymbol{a} \times \boldsymbol{b})_i = \sum_j \sum_k \varepsilon_{i j k} a_j b_k
    stable_ref
    wikidata:literal:16:(\boldsymbol{a} \times \boldsymbol{b})_i = \sum_j \sum_k \varepsilon_{i j k} a_j b_k
    node_kind
    wikidata_literal
    plane
    provider_observed
  • b_i — Literal value
    Technical details
    node_id
    wikidata:literal:17:b_i
    stable_ref
    wikidata:literal:17:b_i
    node_kind
    wikidata_literal
    plane
    provider_observed
  • square brackets — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q2751137
    stable_ref
    Q2751137
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q2751137
    provider
    wikidata
    entity_href
    /entries/wikidata/Q2751137

Edges (20)

  • cross product — different from → vector multiplication — Observed provider relationships
    Technical details
    machine_predicate
    P1889
    predicate_ref
    wikidata:property:P1889
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:0:P1889
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • cross product — subclass of → vector multiplication — Observed provider relationships
    Technical details
    machine_predicate
    P279
    predicate_ref
    wikidata:property:P279
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:1:P279
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • cross product — Relationship label not yet available → \boldsymbol{a} — Observed provider relationships
    Technical details
    machine_predicate
    P7235
    predicate_ref
    wikidata:property:P7235
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:2:P7235
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • cross product — Relationship label not yet available → \varepsilon_{i j k} — Observed provider relationships
    Technical details
    machine_predicate
    P7235
    predicate_ref
    wikidata:property:P7235
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:3:P7235
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • cross product — Relationship label not yet available → anticommutativity — Observed provider relationships
    Technical details
    machine_predicate
    P1552
    predicate_ref
    wikidata:property:P1552
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:4:P1552
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • cross product — Relationship label not yet available → × — Observed provider relationships
    Technical details
    machine_predicate
    P913
    predicate_ref
    wikidata:property:P913
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:5:P913
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • cross product — Relationship label not yet available → Wikipedia:Vital articles/Level/4 — Observed provider relationships
    Technical details
    machine_predicate
    P5008
    predicate_ref
    wikidata:property:P5008
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:6:P5008
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • cross product — Relationship label not yet available → \boldsymbol{b} — Observed provider relationships
    Technical details
    machine_predicate
    P7235
    predicate_ref
    wikidata:property:P7235
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:7:P7235
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • cross product — Relationship label not yet available → WikiProject Mathematics — Observed provider relationships
    Technical details
    machine_predicate
    P6104
    predicate_ref
    wikidata:property:P6104
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:8:P6104
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • cross product — Relationship label not yet available → — — Observed provider relationships
    Technical details
    machine_predicate
    P8864
    predicate_ref
    wikidata:property:P8864
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:9:P8864
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • cross product — Relationship label not yet available → \boldsymbol{a} \times \boldsymbol{b} = \begin{pmatrix} a_y b_z - a_z b_y \\ a_z b_x - a_x b_z \\ a_x b_y - a_y b_x \end{pmatrix} — Observed provider relationships
    Technical details
    machine_predicate
    P2534
    predicate_ref
    wikidata:property:P2534
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:10:P2534
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • cross product — Relationship label not yet available → a_i — Observed provider relationships
    Technical details
    machine_predicate
    P7235
    predicate_ref
    wikidata:property:P7235
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:11:P7235
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • cross product — described by source → ISO 80000-2:2019 Quantities and units — Part 2: Mathematics — Observed provider relationships
    Technical details
    machine_predicate
    P1343
    predicate_ref
    wikidata:property:P1343
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:12:P1343
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • cross product — Relationship label not yet available → \boldsymbol{a} \times \boldsymbol{b} — Observed provider relationships
    Technical details
    machine_predicate
    P7235
    predicate_ref
    wikidata:property:P7235
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:13:P7235
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • cross product — Commons category → Cross product — Observed provider relationships
    Technical details
    machine_predicate
    P373
    predicate_ref
    wikidata:property:P373
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:14:P373
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • cross product — subclass of → binary operation — Observed provider relationships
    Technical details
    machine_predicate
    P279
    predicate_ref
    wikidata:property:P279
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:15:P279
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • cross product — Relationship label not yet available → (\boldsymbol{a} \times \boldsymbol{b})_i = \sum_j \sum_k \varepsilon_{i j k} a_j b_k — Observed provider relationships
    Technical details
    machine_predicate
    P2534
    predicate_ref
    wikidata:property:P2534
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:16:P2534
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • cross product — Relationship label not yet available → b_i — Observed provider relationships
    Technical details
    machine_predicate
    P7235
    predicate_ref
    wikidata:property:P7235
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:17:P7235
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • vector multiplication — different from → cross product — Observed provider relationships
    Technical details
    machine_predicate
    P1889
    predicate_ref
    wikidata:property:P1889
    provider
    wikidata
    provider_direction
    incoming
    plane
    provider_observed
    edge_id
    wikidata:relation:18:P1889
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • square brackets — Relationship label not yet available → cross product — Observed provider relationships
    Technical details
    machine_predicate
    P366
    predicate_ref
    wikidata:property:P366
    provider
    wikidata
    provider_direction
    incoming
    plane
    provider_observed
    edge_id
    wikidata:relation:19:P366
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7

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