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Isomorphism - Wikipedia
https://en.wikipedia.org/wiki/Isomorphism
WebIn mathematics, an isomorphism is a structure-preserving mapping between two structures of the same type that can be reversed by an inverse mapping. Two mathematical structures are isomorphic if an isomorphism exists between them. The word isomorphism is derived from the Ancient Greek: ἴσος isos "equal", and μορφή morphe "form" or "shape".
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Isomorphic Definition & Meaning - Merriam-Webster
https://www.merriam-webster.com/dictionary/isomorphic
Web1. a. : being of identical or similar form, shape, or structure. isomorphic crystals. b. : having sporophytic and gametophytic generations alike in size and shape. 2. : related by an isomorphism. isomorphic mathematical rings. isomorphically. ˌī-sə-ˈmȯr-fi-k (ə-)lē. adverb. Examples of isomorphic in a Sentence.
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ISOMORPHIC | English meaning - Cambridge Dictionary
https://dictionary.cambridge.org/dictionary/english/isomorphic
Webadjective [ before noun ] uk / ˈaɪsəmɔːfɪk / us. Add to word list. the same or similar in structure or shape: isomorphic arrangement/pressure/power Outsourcing may create …
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Isomorphism | Group Theory, Algebraic Structures ... - Britannica
https://www.britannica.com/science/isomorphism-mathematics
WebMar 20, 2024 · Isomorphism, in modern algebra, a one-to-one correspondence (mapping) between two sets that preserves binary relationships between elements of the sets. For example, the set of natural numbers can be mapped onto the set of even natural numbers by multiplying each natural number by 2. The binary.
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Isomorphism -- from Wolfram MathWorld
https://mathworld.wolfram.com/Isomorphism.html
WebMar 15, 2024 · Informally, an isomorphism is a map that preserves sets and relations among elements. " is isomorphic to " is written . Unfortunately, this symbol is also used to denote geometric congruence . An isomorphism from a set of elements onto itself is called an automorphism .
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5.6: Isomorphisms - Mathematics LibreTexts
https://math.libretexts.org/Bookshelves/Linear_Algebra/A_First_Course_in_Linear_Algebra_(Kuttler)/05%3A_Linear_Transformations/5.06%3A_Isomorphisms
WebSep 17, 2022 · Theorem \(\PageIndex{1}\): Isomorphic Subspaces. Suppose \(V\) and \(W\) are two subspaces of \(\mathbb{R}^n\). Then the two subspaces are isomorphic if and only if they have the same dimension. In the case that the two subspaces have the same dimension, then for a linear map \(T:V\rightarrow W\), the following are equivalent. \(T\) is …
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ISOMORPHIC | definition in the Cambridge English Dictionary
https://dictionary.cambridge.org/us/dictionary/english/isomorphic
WebIn visceral heterotaxy, from the stance of the heart, the atrial appendages are isomorphic (usually known as isomerism). From the Cambridge English Corpus. Two database …
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Isomorphism Definition & Meaning - Merriam-Webster
https://www.merriam-webster.com/dictionary/isomorphism
Web1. : the quality or state of being isomorphic: such as. a. : similarity in organisms of different ancestry resulting from convergence. b. : similarity of crystalline form between chemical compounds. 2. : a one-to-one correspondence between two mathematical sets.
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11.7: Isomorphisms - Mathematics LibreTexts
https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Applied_Discrete_Structures_(Doerr_and_Levasseur)/11%3A_Algebraic_Structures/11.07%3A_Isomorphisms
WebAug 17, 2021 · The best way to prove that two groups are not isomorphic is to find a true statement about one group that is not true about the other group. We illustrate this method in the following checklist that you can apply to most pairs …
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11.4: Graph Isomorphisms - Mathematics LibreTexts
https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Combinatorics_(Morris)/03%3A_Graph_Theory/11%3A_Basics_of_Graph_Theory/11.04%3A_Graph_Isomorphisms
WebJul 12, 2021 · Definition: Isomorphism. Two graphs \ (G_1 = (V_1, E_1)\) and \ (G_2 = (V_2, E_2)\) are isomorphic if there is a bijection (a one-to-one, onto map) \ (\varphi\) from \ (V_1\) to \ (V_2\) such that. \ [\ {v, w\} ∈ E_1 ⇔ \ {\varphi (v), \varphi (w)\} ∈ E_2.\] In this case, we call \ (\varphi\) an isomorphism from \ (G_1\) to \ (G_2\). Notation.
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