{
  "aliases": [
    "frechet-derivative",
    "strong-derivative"
  ],
  "backlinks": [
    {
      "field": "defines",
      "target": "08EVNYZF42"
    },
    {
      "field": "uses",
      "target": "0B6QWX3086"
    },
    {
      "field": "uses",
      "target": "0F32S73FJN"
    },
    {
      "field": "uses",
      "target": "1YDR94WQMZ"
    },
    {
      "field": "uses",
      "target": "2K13M9FBAN"
    },
    {
      "field": "uses",
      "target": "3PGXH0T1K6"
    },
    {
      "field": "uses",
      "target": "8D5Y3JNF09"
    },
    {
      "field": "uses",
      "target": "9ZCCXT3KKP"
    },
    {
      "field": "uses",
      "target": "BTM6WJ0A52"
    },
    {
      "field": "uses",
      "target": "DFXSJH9TY4"
    },
    {
      "field": "uses",
      "target": "EPXNCSP2MN"
    },
    {
      "field": "uses",
      "target": "FZXRWKD430"
    },
    {
      "field": "uses",
      "target": "KA3V66S6F5"
    },
    {
      "field": "uses",
      "target": "M218MWZ62X"
    },
    {
      "field": "uses",
      "target": "P4X779XNEA"
    },
    {
      "field": "uses",
      "target": "PDXR52YGPD"
    },
    {
      "field": "uses",
      "target": "Q7QK3PF806"
    },
    {
      "field": "uses",
      "target": "VB95VVVDM8"
    },
    {
      "field": "about",
      "target": "3PGXH0T1K6"
    },
    {
      "field": "about",
      "target": "BTM6WJ0A52"
    },
    {
      "field": "about",
      "target": "M218MWZ62X"
    },
    {
      "field": "about",
      "target": "Q7QK3PF806"
    }
  ],
  "body": "\n## Summary\n\nThe Fréchet derivative of a map $f$ between normed vector spaces at a point $x$ is a bounded linear map. It best approximates $f(x + h) - f(x)$ for small $h$.\nIt extends the derivative of one-variable calculus to maps between normed spaces, which can have infinite dimension.\nFor maps between Euclidean spaces it is the [[total derivative|0FNKFT8H6E]].\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "aliases": [
      "frechet-derivative",
      "strong-derivative"
    ],
    "inventory": [
      "HJFMD7QKFR"
    ],
    "kind": "concept",
    "msc": [
      "46G05"
    ],
    "name": "Fréchet derivative",
    "same_as": {
      "wikidata": "Q1305350",
      "wikipedia": "Fréchet derivative"
    },
    "sources": [
      {
        "locator": "lead section",
        "url": "https://en.wikipedia.org/wiki/Fr%C3%A9chet_derivative"
      }
    ],
    "tag": "06EH97V2A7",
    "uses": [
      "0FNKFT8H6E"
    ]
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/06EH97V2A7/",
  "links": [
    {
      "field": "uses",
      "target": "0FNKFT8H6E"
    }
  ],
  "markdown": "https://tamnd.github.io/math2/node/06EH97V2A7.md",
  "msc": [
    "46G05"
  ],
  "name": "Fréchet derivative",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/06E/06EH97V2A7.md",
  "status": null,
  "tag": "06EH97V2A7",
  "uri": "m2://06EH97V2A7",
  "url": "https://tamnd.github.io/math2/wiki/frechet-derivative/",
  "writing": {
    "tag": "06EH97V2A7",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 0,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
        "have": 0,
        "want": 1
      }
    ]
  }
}
