See biinvariant in All languages combined, or Wiktionary
{ "etymology_templates": [ { "args": { "1": "en", "2": "bi", "3": "invariant" }, "expansion": "bi- + invariant", "name": "prefix" } ], "etymology_text": "From bi- + invariant.", "head_templates": [ { "args": { "1": "-" }, "expansion": "biinvariant (not comparable)", "name": "en-adj" } ], "lang": "English", "lang_code": "en", "pos": "adj", "senses": [ { "categories": [ { "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w" }, { "kind": "other", "name": "English terms prefixed with bi-", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with entries", "parents": [], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Mathematics", "orig": "en:Mathematics", "parents": [ "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "examples": [ { "ref": "2015, Valera Berestovskii, Irina Zubareva, Victor Svirkin, “The spectrum of the Laplace operator on connected compact simple Lie groups of rank 3”, in arXiv:", "text": "In this paper we give explicit calculations of the Laplace operator's spectrum for smooth real or complex functions on all connected compact simple Lie groups of rank 3 with biinvariant Riemannian metric and establish a connection of these formulas with the number theory and ternary and binary quadratic forms..", "type": "quote" } ], "glosses": [ "Both left-invariant and right-invariant." ], "id": "en-biinvariant-en-adj-6tn4jQ35", "links": [ [ "mathematics", "mathematics" ] ], "raw_glosses": [ "(mathematics) Both left-invariant and right-invariant." ], "tags": [ "not-comparable" ], "topics": [ "mathematics", "sciences" ] } ], "word": "biinvariant" }
{ "etymology_templates": [ { "args": { "1": "en", "2": "bi", "3": "invariant" }, "expansion": "bi- + invariant", "name": "prefix" } ], "etymology_text": "From bi- + invariant.", "head_templates": [ { "args": { "1": "-" }, "expansion": "biinvariant (not comparable)", "name": "en-adj" } ], "lang": "English", "lang_code": "en", "pos": "adj", "senses": [ { "categories": [ "English adjectives", "English entries with incorrect language header", "English lemmas", "English terms prefixed with bi-", "English terms with quotations", "English uncomparable adjectives", "Pages with 1 entry", "Pages with entries", "en:Mathematics" ], "examples": [ { "ref": "2015, Valera Berestovskii, Irina Zubareva, Victor Svirkin, “The spectrum of the Laplace operator on connected compact simple Lie groups of rank 3”, in arXiv:", "text": "In this paper we give explicit calculations of the Laplace operator's spectrum for smooth real or complex functions on all connected compact simple Lie groups of rank 3 with biinvariant Riemannian metric and establish a connection of these formulas with the number theory and ternary and binary quadratic forms..", "type": "quote" } ], "glosses": [ "Both left-invariant and right-invariant." ], "links": [ [ "mathematics", "mathematics" ] ], "raw_glosses": [ "(mathematics) Both left-invariant and right-invariant." ], "tags": [ "not-comparable" ], "topics": [ "mathematics", "sciences" ] } ], "word": "biinvariant" }
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This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2025-01-08 from the enwiktionary dump dated 2025-01-01 using wiktextract (9a96ef4 and 4ed51a5). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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