{
  "aliases": [
    "grassmann-algebra"
  ],
  "backlinks": [
    {
      "field": "defines",
      "target": "08HK38GCSM"
    }
  ],
  "body": "\n## Summary\n\nThe exterior algebra of a vector space is the associative algebra generated by the space in which the square of every vector is zero.\n",
  "commit": "6ac761d40018146541484a9e8b9eafd6ecc303dc",
  "front": {
    "aliases": [
      "grassmann-algebra"
    ],
    "kind": "concept",
    "msc": [
      "15A75"
    ],
    "name": "Exterior algebra",
    "same_as": {
      "wikidata": "Q1196652",
      "wikipedia": "Exterior algebra"
    },
    "sources": [
      {
        "locator": "Formal definition",
        "url": "https://en.wikipedia.org/wiki/Exterior_algebra"
      }
    ],
    "tag": "0MDMZ965VE"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/0MDMZ965VE/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/0MDMZ965VE.md",
  "msc": [
    "15A75"
  ],
  "name": "Exterior algebra",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0MD/0MDMZ965VE.md",
  "status": null,
  "tag": "0MDMZ965VE",
  "uri": "m2://0MDMZ965VE",
  "url": "https://math2.tamnd.com/wiki/exterior-algebra/",
  "writing": {
    "tag": "0MDMZ965VE",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 0,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
        "have": 0,
        "want": 1
      }
    ]
  }
}