implicit function theorem
theorem that, under a mild condition on the partial derivatives, the set of zeros of a system of equations is locally the graph of a function
| rdfs:label |
"implicit function theorem"@en
|
|
skos:alt |
"Satz über die Umkehrfunktion"@de
"Satz über die inverse Funktion"@de
"Satz über implizite Funktionen"@de
"Satz über lokale Umkehrbarkeit"@de
|
| schema:description |
"theorem that, under a mild condition on the partial derivatives, the set of zeros of a system of equations is locally the graph of a function"@en
|
|
schema:date |
"2026-09-07T10:46:54+00:00"^^xsd:dateTime |
| schema:version | 2541642881 |
| wikibase:identifiers | 6 |
| wikibase:sitelinks | 21 |
| wikibase:statements | 14 |
| p:P10283 | wd:statement/Q848375-56F707B9-5E09-4AE1-B23C-11437A1AB20B |
| p:P13591 | wd:statement/Q848375-554832A5-1D67-4CDC-B12F-8A1858BFC085 |
| p:P18 | wd:statement/Q848375-9efc64a1-424c-137b-db36-3d195e3d47a8 |
| p:P1889 | wd:statement/Q848375-7f72c82a-43d1-ed7e-11ec-fc0cf47c0f16 |
| p:P227 | wd:statement/Q848375-46e52a3d-4dfb-54b8-115a-57ebf6c35c37 |
| p:P2384 | wd:statement/Q848375-2e40df37-49fc-aeae-702f-e49d8b140c84 |
| p:P2534 | wd:statement/Q848375-4b8717c0-4e1f-9b54-a5fb-98d5f8084123 |
| p:P2579 | wd:statement/Q848375-E513974A-3806-4EAF-98AC-14598466AE9C |
| p:P2812 | wd:statement/Q848375-45faf53f-4e37-f84c-1019-a2c1485cc626 |
| p:P31 | wd:statement/Q848375-9C7BFF20-F0AB-4134-8466-AA62966C2C1D |
| p:P361 | wd:statement/Q848375-5C1F510C-C793-4A56-91CE-33E4E3E020EF |
| p:P6104 | wd:statement/Q848375-CADD12B8-2B59-4D88-A8A8-A1D9E8148113 |
| p:P6366 | wd:statement/Q848375-48F3EB1A-3CAC-4700-B1A1-6C2A027C37E9 |
| p:P646 | wd:statement/Q848375-091236B4-369B-431E-B2EA-41A65E7905F2 |
|
p:direct- |
<https:/ |
|
p:direct- |
<https:/ |
| wdt:P10283 | "C138578839" |
| wdt:P13591 | "concept/2a5db441-7cca-4968-b594-d60615d959b3" |
| wdt:P18 |
<http:/ |
| wdt:P1889 | inverse function theorem |
| wdt:P227 | "4570203-2" |
| wdt:P2384 | implicit function |
| wdt:P2534 | "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><mi>f</mi><mo stretchy="false">∈</mo><msup><mrow data-mjx-texclass="ORD"><mi data-mjx-variant="-tex-calligraphic">𝒞</mi></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msup><mo stretchy="false">(</mo><msup><mrow data-mjx-texclass="ORD"><mi>ℝ</mi></mrow><mrow data-mjx-texclass="ORD"><mi>m</mi></mrow></msup><mo stretchy="false">×</mo><msup><mrow data-mjx-texclass="ORD"><mi>ℝ</mi></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msup><mo>,</mo><msup><mrow data-mjx-texclass="ORD"><mi>ℝ</mi></mrow><mrow data-mjx-texclass="ORD"><mi>m</mi></mrow></msup><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN"></mo><mi>det</mi><mo>⁡</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo stretchy="false">)</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>x</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo stretchy="false">)</mo></mrow></mrow></msub><mo stretchy="false">≠</mo><mn>0</mn><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mo>⟹</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mi mathvariant="normal">∃</mi><mo stretchy="false">(</mo><mi>b</mi><mo stretchy="false">∈</mo><mi>U</mi><mo stretchy="false">⊂</mo><msup><mrow data-mjx-texclass="ORD"><mi>ℝ</mi></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msup><mo stretchy="false">)</mo><mi mathvariant="normal">∃</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">:</mo><mi>U</mi><mo stretchy="false" accent="false">→</mo><msup><mrow data-mjx-texclass="ORD"><mi>ℝ</mi></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msup><mo stretchy="false">)</mo><mo stretchy="false">:</mo><mi>g</mi><mo stretchy="false">(</mo><mi>b</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>a</mi><mo stretchy="false">∧</mo><mi mathvariant="normal">∀</mi><mi>x</mi><mo stretchy="false">∈</mo><mi>U</mi><mo stretchy="false">:</mo><mi>f</mi><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>,</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mn>0</mn></mtd></mtr></mtable></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| wdt:P2579 | calculus |
| wdt:P2812 | "ImplicitFunctionTheorem" |
| wdt:P31 | theorem |
| wdt:P361 | list of theorems |
| wdt:P6104 | WikiProject Mathematics |
| wdt:P6366 | "138578839" |
| wdt:P646 | "/m/02s4mn" |
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