{
  "id": "2403.05214",
  "version": "v1",
  "published": "2024-03-08T10:56:29.000Z",
  "updated": "2024-03-08T10:56:29.000Z",
  "title": "A note on the singular value decomposition of idempotent and involutory matrices",
  "authors": [
    "Heike Faßbender",
    "Martin Halwaß"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "It is known that singular values of idempotent matrices are either zero or larger or equal to one \\cite{HouC63}. We state exactly how many singular values greater than one, equal to one, and equal to zero there are. Moreover, we derive a singular value decomposition of idempotent matrices which reveals a tight relationship between its left and right singular vectors. The same idea is used to augment a discovery regarding the singular values of involutory matrices as presented in \\cite{FasH20}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-08T10:56:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A24"
    ],
    "keywords": [
      "singular value decomposition",
      "involutory matrices",
      "idempotent matrices",
      "singular values greater",
      "right singular vectors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}