"spectral theory" meaning in English

{
  "forms": [
    {
      "form": "spectral theories",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "spectral theory (plural spectral theories)",
      "name": "en-noun"
    }
  ],
  "hyphenation": [
    "spec‧tral"
  ],
  "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"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "Those theories extending the eigenvalue and eigenvector theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces."
      ],
      "hypernyms": [
        {
          "word": "theory"
        }
      ],
      "id": "en-spectral_theory-en-noun-0CFxyMwQ",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "eigenvalue",
          "eigenvalue"
        ],
        [
          "eigenvector",
          "eigenvector"
        ],
        [
          "square matrix",
          "square matrix"
        ],
        [
          "operator",
          "operator"
        ]
      ],
      "raw_glosses": [
        "(mathematics) Those theories extending the eigenvalue and eigenvector theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "sounds": [
    {
      "ipa": "/ˈspɛktɹ(ə)l ˈθɪəɹi/"
    },
    {
      "audio": "LL-Q1860 (eng)-StuckInLagToad-spectral theory.wav",
      "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/c/c3/LL-Q1860_%28eng%29-StuckInLagToad-spectral_theory.wav/LL-Q1860_%28eng%29-StuckInLagToad-spectral_theory.wav.mp3",
      "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/c/c3/LL-Q1860_%28eng%29-StuckInLagToad-spectral_theory.wav/LL-Q1860_%28eng%29-StuckInLagToad-spectral_theory.wav.ogg",
      "tags": [
        "Southern-US"
      ],
      "text": "Audio (Southern US)"
    }
  ],
  "word": "spectral theory"
}

{
  "forms": [
    {
      "form": "spectral theories",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "spectral theory (plural spectral theories)",
      "name": "en-noun"
    }
  ],
  "hypernyms": [
    {
      "word": "theory"
    }
  ],
  "hyphenation": [
    "spec‧tral"
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with IPA pronunciation",
        "English terms with audio links",
        "en:Mathematics"
      ],
      "glosses": [
        "Those theories extending the eigenvalue and eigenvector theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "eigenvalue",
          "eigenvalue"
        ],
        [
          "eigenvector",
          "eigenvector"
        ],
        [
          "square matrix",
          "square matrix"
        ],
        [
          "operator",
          "operator"
        ]
      ],
      "raw_glosses": [
        "(mathematics) Those theories extending the eigenvalue and eigenvector theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "sounds": [
    {
      "ipa": "/ˈspɛktɹ(ə)l ˈθɪəɹi/"
    },
    {
      "audio": "LL-Q1860 (eng)-StuckInLagToad-spectral theory.wav",
      "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/c/c3/LL-Q1860_%28eng%29-StuckInLagToad-spectral_theory.wav/LL-Q1860_%28eng%29-StuckInLagToad-spectral_theory.wav.mp3",
      "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/c/c3/LL-Q1860_%28eng%29-StuckInLagToad-spectral_theory.wav/LL-Q1860_%28eng%29-StuckInLagToad-spectral_theory.wav.ogg",
      "tags": [
        "Southern-US"
      ],
      "text": "Audio (Southern US)"
    }
  ],
  "word": "spectral theory"
}