In mathematics, an isomorphism is a structure-preserving mapping or morphism between two structures of the same type that can be reversed by an inverse mapping. Two mathematical structures are …

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 …

Dec 3, 2025 · Isomorphism is a very general concept that appears in several areas of mathematics. The word derives from the Greek iso, meaning "equal," and morphosis, meaning "to form" or "to shape." …

Dec 18, 2021 · 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 …

Category theory makes this precise and shifts the emphasis to the 'isomorphism' - the way in which we match up these two objects, to see that they look the same.

The meaning of ISOMORPHISM is the quality or state of being isomorphic.

Jul 23, 2025 · In the study of algebraic structures, group isomorphisms and automorphisms play a fundamental role. By defining internal symmetries inside a group (automorphisms) and when two …

Mar 5, 2012 · An isomorphism is a correspondence (relation) between objects or systems of objects expressing the equality of their structures in some sense.

Dec 1, 2025 · In the alternative derivation , we used the intuition that an isomorphism is a linear map that "preserves bases". This means that bases are sent to bases and linear combinations are preserved.

Consider two subspaces \ (V\) and \ (W\), and suppose there exists an isomorphism mapping one to the other. In this way the two subspaces are related, which we can write as \ (V \sim W\).