Here an isomorphism just a bijective linear map between linear spaces. Two linear spaces are isomorphic if there exists a linear isomorphism between them.

Aug 4, 2021 · Whenever a problem or question of isomorphism comes up I am clueless as to what they mean. From my understanding an isomorphism is in terms of graph theory where it is the same thing …

11 I know that the concept of being isomorphic depends on the category we are working in. So specifically when we are building a theory, like when we define the natural numbers, or the real …

Nov 28, 2015 · Isomorphism only means what it says, a homomorphism which is bijective. As a consequence two isomorphic groups share many properties, number of elements of a specific order, …

Isomorphisms capture "equality" between objects in the sense of the structure you are considering. For example, $2 \mathbb {Z} \ \cong \mathbb {Z}$ as groups, meaning we could re-label the elements in …

Mar 10, 2019 · Are these two graphs isomorphic? According to Bruce Schneier: "A graph is a network of lines connecting different points. If two graphs are identical except for the names of the points, they …

Feb 11, 2016 · So all that treating isomorphic objects as equal is completely justified in homotopy type theory. By itself that wouldn't be that exciting, but homotopy type theory is a (fairly minor in some …

The word isomorphism is related to category, in which you work. For example, if you work in the category $\mathbf {Top}$ of topological spaces, the words isomorphism and homeomorphism are …

I have just started studying graph theory and having trouble with understanding the difference b/w isomorphism and equality of two graphs.According what I have studied so far, I am able to conclude...

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 …