{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "0MM085RX00"
    }
  ],
  "body": "\n## Summary\n\nThe product of two vector spaces over the same field is the set of pairs, with addition and scalar multiplication done in each component.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "inventory": [
      "889YSB2XEX"
    ],
    "kind": "concept",
    "msc": [
      "15A03"
    ],
    "name": "Product of vector spaces",
    "sources": [
      {
        "locator": "Construction for two vector spaces",
        "url": "https://en.wikipedia.org/wiki/Direct_sum_of_modules"
      }
    ],
    "specializes": [
      "000AYPA9AJ"
    ],
    "tag": "0EX2HPXPJ6"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/0EX2HPXPJ6/",
  "links": [
    {
      "field": "specializes",
      "target": "000AYPA9AJ"
    }
  ],
  "markdown": "https://tamnd.github.io/math2/node/0EX2HPXPJ6.md",
  "msc": [
    "15A03"
  ],
  "name": "Product of vector spaces",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0EX/0EX2HPXPJ6.md",
  "status": null,
  "tag": "0EX2HPXPJ6",
  "uri": "m2://0EX2HPXPJ6",
  "url": "https://tamnd.github.io/math2/wiki/product-of-vector-spaces/",
  "writing": {
    "tag": "0EX2HPXPJ6",
    "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
      }
    ]
  }
}