{
  "id": "1409.5535",
  "version": "v1",
  "published": "2014-09-19T07:40:53.000Z",
  "updated": "2014-09-19T07:40:53.000Z",
  "title": "Further refinements of the Cauchy-Schwarz inequality for matrices",
  "authors": [
    "Mojtaba Bakherad"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $A, B$ and $X$ be $n\\times n$ matrices such that $A, B$ are positive semidefinite. We present some refinements of the matrix Cauchy-Schwarz inequality by using some integration techniques and various refinements of the Hermite--Hadamard inequality. In particular, we establish the inequality \\begin{align*} |||\\,|A^{1\\over2}XB^{1\\over2}|^r|||^2&\\leq|||\\,|A^{t}XB^{1-s}|^r||| \\,\\,\\,|||\\,|A^{1-t}XB^{s}|^r|||\\\\& \\leq\\max \\{|||\\,|AX|^r||| \\,\\,\\,|||\\,|XB|^r|||,|||\\,|AXB|^r||| \\,\\,\\,|||\\,|X|^r|||\\}, \\end{align*} where $s,t\\in[0,1]$ and $r\\geq0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-19T07:40:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "refinements",
      "matrix cauchy-schwarz inequality",
      "hermite-hadamard inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.5535B"
    }
  }
}