See semi-norm on Wiktionary
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"2": "semi",
"3": "norm"
},
"expansion": "semi- + norm",
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],
"etymology_text": "From semi- + norm.",
"forms": [
{
"form": "semi-norms",
"tags": [
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"derived": [
{
"word": "semi-normed"
},
{
"word": "seminormed"
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"glosses": [
"A function denoted ∥v∥ that maps a vector v to a non-negative value such that ∥cv∥ = |c|.∥v∥, where c is a scalar, and ∥v + w∥ ≤ ∥v∥ + ∥w∥ (the triangle inequality); the condition that ∥v∥ = 0 implies that v = 0 is not required, but when it holds, the semi-norm is a norm."
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"id": "en-semi-norm-en-noun-uqAdB1MH",
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"(mathematical analysis) A function denoted ∥v∥ that maps a vector v to a non-negative value such that ∥cv∥ = |c|.∥v∥, where c is a scalar, and ∥v + w∥ ≤ ∥v∥ + ∥w∥ (the triangle inequality); the condition that ∥v∥ = 0 implies that v = 0 is not required, but when it holds, the semi-norm is a norm."
],
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"sense": "in analysis",
"word": "gauge"
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{
"word": "seminorm"
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"translations": [
{
"code": "de",
"lang": "German",
"sense": "a function that maps a vector to a non-negative value",
"tags": [
"feminine"
],
"word": "Halbnorm"
},
{
"code": "de",
"lang": "German",
"sense": "a function that maps a vector to a non-negative value",
"tags": [
"feminine"
],
"word": "Seminorm"
},
{
"code": "it",
"lang": "Italian",
"sense": "a function that maps a vector to a non-negative value",
"tags": [
"feminine"
],
"word": "norma"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "a function that maps a vector to a non-negative value",
"word": "seminorm"
}
]
}
],
"word": "semi-norm"
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{
"word": "seminormed"
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"etymology_text": "From semi- + norm.",
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"A function denoted ∥v∥ that maps a vector v to a non-negative value such that ∥cv∥ = |c|.∥v∥, where c is a scalar, and ∥v + w∥ ≤ ∥v∥ + ∥w∥ (the triangle inequality); the condition that ∥v∥ = 0 implies that v = 0 is not required, but when it holds, the semi-norm is a norm."
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"(mathematical analysis) A function denoted ∥v∥ that maps a vector v to a non-negative value such that ∥cv∥ = |c|.∥v∥, where c is a scalar, and ∥v + w∥ ≤ ∥v∥ + ∥w∥ (the triangle inequality); the condition that ∥v∥ = 0 implies that v = 0 is not required, but when it holds, the semi-norm is a norm."
],
"topics": [
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"synonyms": [
{
"sense": "in analysis",
"word": "gauge"
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{
"word": "seminorm"
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],
"translations": [
{
"code": "de",
"lang": "German",
"sense": "a function that maps a vector to a non-negative value",
"tags": [
"feminine"
],
"word": "Halbnorm"
},
{
"code": "de",
"lang": "German",
"sense": "a function that maps a vector to a non-negative value",
"tags": [
"feminine"
],
"word": "Seminorm"
},
{
"code": "it",
"lang": "Italian",
"sense": "a function that maps a vector to a non-negative value",
"tags": [
"feminine"
],
"word": "norma"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "a function that maps a vector to a non-negative value",
"word": "seminorm"
}
],
"word": "semi-norm"
}
Download raw JSONL data for semi-norm meaning in All languages combined (2.5kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-12-15 from the enwiktionary dump dated 2024-12-04 using wiktextract (8a39820 and 4401a4c). 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.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.