terminology - What does "isomorphic" mean in linear algebra ...
Here an isomorphism just a bijective linear map between linear spaces. Two linear spaces are isomorphic if there exists a linear isomorphism between them.
abstract algebra - What is exactly the meaning of being …
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 …
What does it mean when two Groups are isomorphic?
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 …
What's the difference between isomorphism and homeomorphism?
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 these two graphs isomorphic? Why/Why not?
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 …
Difference between "≈", "≃", and "≅" - Mathematics Stack Exchange
In mathematical notation, what are the usage differences between the various approximately-equal signs "≈", "≃", and "≅"? The Unicode standard lists all of them inside the Mathematical …
basic difference between canonical isomorphism and isomorphims
Apr 26, 2019 · What is the basic difference between canonical isomorphism and isomorphims? I need some basic analysis. As far as I consider on canonical isomorphism means a similarity …
Are the groups $(\\mathbb{C},+)$ and $(\\mathbb{R},+)
$\bf C$ and $\bf R$ are isomorphic as vector spaces over $\bf Q$ (take uncountably infinite transcendence bases) so they are isomorphic as additive groups.
How to tell whether two graphs are isomorphic?
Oct 24, 2017 · Unfortunately, if two graphs have the same Tutte polynomial, that does not guarantee that they are isomorphic. Links See the Wikipedia article on graph isomorphism for …
abstract algebra - When we say two fields are isomorphic, does …
Dec 11, 2018 · Thus two fields are isomorphic if and only if they are isomorphic when considered as rings. But this is a contingent fact, and it's not really what we mean when we say that two …