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- what exactly is an isomorphism? - Mathematics Stack Exchange
An isomorphism within a partial order is an equality If there is an isomorphism between two objects, then they are totally indistinguishable from the perspective of category theory
- What is the difference between homomorphism and isomorphism?
Isomorphism is a bijective homomorphism I see that isomorphism is more than homomorphism, but I don't really understand its power When we hear about bijection, the first thing that comes to mind is topological homeomorphism, but here we are talking about algebraic structures, and topological spaces are not algebraic structures
- linear algebra - Difference between epimorphism, isomorphism . . .
Can somebody please explain me the difference between linear transformations such as epimorphism, isomorphism, endomorphism or automorphism? I would appreciate if somebody can explain the idea with examples or guide to some good source to clear the concept
- Isomorphic groups beyond the isomorphism: is this also true for . . .
2 Each isomorphism has an inverse, which is also an isomorphism between the groups So yes: "being isomorphic" goes beyond the isomorphism in that strict sense What we mean when we say two things in mathematics, not just group theory, are isomorphic is that the algebraic structure remains the same up to a relabelling of all the constituent parts
- terminology - What does isomorphic mean in linear algebra . . .
An isomorphism is a homomorphism that can be reversed; that is, an invertible homomorphism So a vector space isomorphism is an invertible linear transformation
- soft question - What is an Isomorphism: Linear algebra - Mathematics . . .
An isomorphism is a bijective homomorphism "Structure" can mean many different things, but in the context of linear algebra, almost exclusively means the vectorial structure -- i e all those rules about addition and scalar multiplication
- Questions on isomorphism of graphs - Mathematics Stack Exchange
I think testing isomorphism between two graphs can be done by just checking their connectivity without the use of labels However, the definition of isomorphism as a map between two sets forces me to think that elements in each set need to be distinguishable by some use of label Otherwise, how do we express which one is being mapped to which?
- Whats an Isomorphism? - Mathematics Stack Exchange
To expand a bit on what @BrianO said, isomorphisms differ between different kinds of objects Broadly speaking, isomorphisms preserve "structure" between objects, but what this "structure" is depends very much on whether you are talking about groups, vector spaces, algebras, etc Hence it's difficult to say what properties are preserved in general by isomorphisms
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