[{"word":"eigenvalue","phonetic":"/ˈaɪɡənˌvæljuː/","phonetics":[{"text":"/ˈaɪɡənˌvæljuː/","audio":"https://api.dictionaryapi.dev/media/pronunciations/en/eigenvalue-us.mp3","sourceUrl":"https://commons.wikimedia.org/w/index.php?curid=1769655","license":{"name":"BY-SA 3.0","url":"https://creativecommons.org/licenses/by-sa/3.0"}}],"meanings":[{"partOfSpeech":"noun","definitions":[{"definition":"A scalar, \\lambda, such that there exists a non-zero vector x (a corresponding eigenvector) for which the image of x under a given linear operator \\mathrm{A} is equal to the image of x under multiplication by \\lambda; i.e. \\mathrm{A} x = \\lambda x.","synonyms":[],"antonyms":[],"example":"The eigenvalues \\lambda of a square transformation matrix \\mathrm{M} may be found by solving \\det(\\mathrm{M} - \\lambda\\mathrm{I}) = 0."}],"synonyms":["characteristic root","characteristic value","eigenroot","latent value","proper value"],"antonyms":[]}],"license":{"name":"CC BY-SA 3.0","url":"https://creativecommons.org/licenses/by-sa/3.0"},"sourceUrls":["https://en.wiktionary.org/wiki/eigenvalue"]}]