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Definitions from WordNet

Definitions from the Web

Isomorphism

Definition:

Isomorphism is a concept used in various fields, including mathematics and computer science, to describe a relationship between two structures that preserves certain properties, such as shape or structure. It implies a one-to-one correspondence between elements of the two structures.

Mathematics sense:

In mathematics, isomorphism refers to a mapping between two mathematical objects that conserves the relationships between their respective elements. It determines if two structures are essentially the same, but may differ in their representation. For example, in group theory, an isomorphism between two groups means they have the same group structure despite potentially distinct elements and operations.

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Computer Science sense:

In computer science, isomorphism refers to the similarity between two data structures or computational models, especially in terms of their performance characteristics. It often relates to efficiently converting between different representations of the same data. An example is graph isomorphism, which determines if two graphs have the same structural properties, even if their node and edge labels differ.

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Sample Sentences:

1. The isomorphism between the two mathematical structures was evident through the preserving of their algebraic properties.
2. In computer graphics, isomorphism allows for seamless transformation between different representations of 3D models.
3. The study of group isomorphisms is fundamental in understanding the equivalence of different algebraic structures.