See eigenvalue in All languages combined, or Wiktionary
Download JSON data for eigenvalue meaning in English (9.3kB)
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"text": "The eigenvalues #x5C;lambda of a square transformation matrix #x5C;mathrm#x7B;M#x7D; may be found by solving #x5C;det(#x5C;mathrm#x7B;M#x7D;-#x5C;lambda#x5C;mathrm#x7B;I#x7D;)#x3D;0.",
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"text": "In the extension, one associates eigenvalues, sets of scalars, with arrays of matrices by considering the singularity of linear combinations of the matrices in the various rows, involving the same coefficients in each case. Attention to this area was called in the early l920's by R. D. Carmichael, who pointed out in addition the enormous variety of mixed eigenvalue problems with several parameters.",
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"text": "For many quantum-mechanical problems it is important to investigate the change of eigenvalues and eigenfunctions with the continuous change of one or more parameters. The case in which one knows the eigenvalues and eigenfunctions for two special values of the parameters, and is interested in the region in between is particularly interesting.",
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"A scalar, λ, such that there exists a non-zero vector x (a corresponding eigenvector) for which the image of x under a given linear operator A is equal to the image of x under multiplication by λ; i.e. Ax=λx."
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"(linear algebra) A scalar, λ, such that there exists a non-zero vector x (a corresponding eigenvector) for which the image of x under a given linear operator A is equal to the image of x under multiplication by λ; i.e. Ax=λx."
],
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"sense": "scalar multiplier of an eigenvector",
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],
"word": "Eigenwert"
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{
"code": "el",
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"word": "עֵרֶךְ עַצְמִי"
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"sense": "scalar multiplier of an eigenvector",
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"word": "固有値"
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"sense": "scalar multiplier of an eigenvector",
"word": "tikrinė reikšmė"
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"code": "fa",
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"word": "مقدار ویژه"
},
{
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"sense": "scalar multiplier of an eigenvector",
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"feminine"
],
"word": "wartość własna"
},
{
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{
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"word": "eigenvalue"
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"text": "For many quantum-mechanical problems it is important to investigate the change of eigenvalues and eigenfunctions with the continuous change of one or more parameters. The case in which one knows the eigenvalues and eigenfunctions for two special values of the parameters, and is interested in the region in between is particularly interesting.",
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"A scalar, λ, such that there exists a non-zero vector x (a corresponding eigenvector) for which the image of x under a given linear operator A is equal to the image of x under multiplication by λ; i.e. Ax=λx."
],
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"code": "cmn",
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"sense": "scalar multiplier of an eigenvector",
"word": "特徵值"
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{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "tèzhēngzhí",
"sense": "scalar multiplier of an eigenvector",
"word": "特征值"
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{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "scalar multiplier of an eigenvector",
"word": "本徵值"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "běnzhēngzhí",
"sense": "scalar multiplier of an eigenvector",
"word": "本征值"
},
{
"code": "cs",
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"sense": "scalar multiplier of an eigenvector",
"tags": [
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"word": "egenværdi"
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{
"code": "nl",
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"sense": "scalar multiplier of an eigenvector",
"tags": [
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],
"word": "eigenwaarde"
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{
"code": "et",
"lang": "Estonian",
"sense": "scalar multiplier of an eigenvector",
"word": "omaväärtus"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "scalar multiplier of an eigenvector",
"word": "ominaisarvo"
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{
"code": "fr",
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"sense": "scalar multiplier of an eigenvector",
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"word": "valeur propre"
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{
"code": "de",
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"sense": "scalar multiplier of an eigenvector",
"tags": [
"masculine"
],
"word": "Eigenwert"
},
{
"code": "el",
"lang": "Greek",
"roman": "idiotimí",
"sense": "scalar multiplier of an eigenvector",
"tags": [
"feminine"
],
"word": "ιδιοτιμή"
},
{
"code": "he",
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"sense": "scalar multiplier of an eigenvector",
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"masculine"
],
"word": "עֵרֶךְ עַצְמִי"
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"sense": "scalar multiplier of an eigenvector",
"tags": [
"neuter"
],
"word": "eigingildi"
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{
"code": "it",
"lang": "Italian",
"sense": "scalar multiplier of an eigenvector",
"tags": [
"masculine"
],
"word": "autovalore"
},
{
"code": "ja",
"lang": "Japanese",
"roman": "koyūchi",
"sense": "scalar multiplier of an eigenvector",
"word": "固有値"
},
{
"code": "lt",
"lang": "Lithuanian",
"sense": "scalar multiplier of an eigenvector",
"word": "tikrinė reikšmė"
},
{
"code": "nb",
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"sense": "scalar multiplier of an eigenvector",
"tags": [
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"sense": "scalar multiplier of an eigenvector",
"tags": [
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],
"word": "eigenverdi"
},
{
"code": "fa",
"lang": "Persian",
"roman": "meqdâr-e viže",
"sense": "scalar multiplier of an eigenvector",
"word": "مقدار ویژه"
},
{
"code": "pl",
"lang": "Polish",
"sense": "scalar multiplier of an eigenvector",
"tags": [
"feminine"
],
"word": "wartość własna"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "scalar multiplier of an eigenvector",
"tags": [
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"masculine"
],
"word": "valor próprio"
},
{
"code": "pt",
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"tags": [
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"word": "autovalor"
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{
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"sense": "scalar multiplier of an eigenvector",
"tags": [
"feminine"
],
"word": "valoare proprie"
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{
"code": "ru",
"lang": "Russian",
"roman": "sóbstvennoje značénije",
"sense": "scalar multiplier of an eigenvector",
"tags": [
"neuter"
],
"word": "со́бственное значе́ние"
},
{
"code": "sk",
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"sense": "scalar multiplier of an eigenvector",
"tags": [
"feminine"
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"word": "vlastná hodnota"
},
{
"code": "es",
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"sense": "scalar multiplier of an eigenvector",
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{
"code": "es",
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"sense": "scalar multiplier of an eigenvector",
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{
"code": "es",
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"sense": "scalar multiplier of an eigenvector",
"tags": [
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],
"word": "egenvärde"
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],
"word": "eigenvalue"
}
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-12 from the enwiktionary dump dated 2024-05-02 using wiktextract (ae36afe and 304864d). 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.