"Grassmann algebra" meaning in All languages combined

{
  "etymology_text": "Named after Hermann Grassmann (1809–1877), a German polymath.",
  "forms": [
    {
      "form": "Grassmann algebras",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Grassmann algebra (plural Grassmann algebras)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
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          "source": "w"
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          "name": "Algebra",
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            "Formal sciences",
            "Sciences",
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            "Fundamental"
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          "source": "w"
        }
      ],
      "examples": [
        {
          "text": "If a Grassmann algebra’s first grade consists of vectors of dimension n, then the algebra has n grades and 2ⁿ dimensions."
        }
      ],
      "glosses": [
        "A direct sum with an exterior product of multivector spaces which are all based on a same underlying finite-dimensional vector space. The associative algebra of sums and exterior products of scalars, vectors, blades, multivectors, and hybrid (i.e., non-homogeneous) sums of multivectors of different grades."
      ],
      "hypernyms": [
        {
          "word": "associative algebra"
        },
        {
          "word": "graded algebra"
        }
      ],
      "id": "en-Grassmann_algebra-en-noun-pjWPKsQ~",
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "direct sum",
          "direct sum"
        ],
        [
          "exterior product",
          "exterior product"
        ],
        [
          "multivector",
          "multivector"
        ],
        [
          "vector space",
          "vector space"
        ],
        [
          "associative algebra",
          "associative algebra"
        ],
        [
          "blade",
          "blade"
        ],
        [
          "homogeneous",
          "homogeneous"
        ]
      ],
      "raw_glosses": [
        "(algebra) A direct sum with an exterior product of multivector spaces which are all based on a same underlying finite-dimensional vector space. The associative algebra of sums and exterior products of scalars, vectors, blades, multivectors, and hybrid (i.e., non-homogeneous) sums of multivectors of different grades."
      ],
      "synonyms": [
        {
          "word": "exterior algebra"
        }
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Hermann Grassmann"
      ]
    }
  ],
  "word": "Grassmann algebra"
}

{
  "etymology_text": "Named after Hermann Grassmann (1809–1877), a German polymath.",
  "forms": [
    {
      "form": "Grassmann algebras",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
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      "expansion": "Grassmann algebra (plural Grassmann algebras)",
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  ],
  "hypernyms": [
    {
      "word": "associative algebra"
    },
    {
      "word": "graded algebra"
    }
  ],
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  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
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        "English countable nouns",
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        "Pages with 1 entry",
        "Pages with entries",
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      "examples": [
        {
          "text": "If a Grassmann algebra’s first grade consists of vectors of dimension n, then the algebra has n grades and 2ⁿ dimensions."
        }
      ],
      "glosses": [
        "A direct sum with an exterior product of multivector spaces which are all based on a same underlying finite-dimensional vector space. The associative algebra of sums and exterior products of scalars, vectors, blades, multivectors, and hybrid (i.e., non-homogeneous) sums of multivectors of different grades."
      ],
      "links": [
        [
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        [
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          "exterior product",
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          "multivector",
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          "associative algebra",
          "associative algebra"
        ],
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          "blade",
          "blade"
        ],
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          "homogeneous",
          "homogeneous"
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      ],
      "raw_glosses": [
        "(algebra) A direct sum with an exterior product of multivector spaces which are all based on a same underlying finite-dimensional vector space. The associative algebra of sums and exterior products of scalars, vectors, blades, multivectors, and hybrid (i.e., non-homogeneous) sums of multivectors of different grades."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Hermann Grassmann"
      ]
    }
  ],
  "synonyms": [
    {
      "word": "exterior algebra"
    }
  ],
  "word": "Grassmann algebra"
}