{
  "id": "2501.05201",
  "version": "v1",
  "published": "2025-01-09T12:52:00.000Z",
  "updated": "2025-01-09T12:52:00.000Z",
  "title": "A study on the 1-$Γ$ inverse of tensors via the M-Product",
  "authors": [
    "Siran Chen",
    "Hongwei Jin",
    "Shaowu Huang",
    "Julio Benítez"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2412.05799",
  "categories": [
    "math.NA",
    "cs.NA",
    "math.RA"
  ],
  "abstract": "In this paper, we will study the issue about the 1-$\\Gamma$ inverse, where $\\Gamma\\in\\{\\dag, D, *\\}$, via the M-product. The aim of the current study is threefold. Firstly, the definition and characteristic of the 1-$\\Gamma$ inverse is introduced. Equivalent conditions for a tensor to be a 1-$\\Gamma$ inverse are established. Secondly, using the singular value decomposition, the corresponding numerical algorithms for computing the 1-$\\Gamma$ inverse are given. Finally, the solutions of the multilinear equations related 1-$\\Gamma$ inverse are studied, and numerical calculations are given to verify our conclusions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-01-09T12:52:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "singular value decomposition",
      "current study",
      "equivalent conditions",
      "multilinear equations",
      "characteristic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}