user84215
I can not understand how to solve it .
Can anybody provide me a hint .
Added: There solution is also given but I could not understand it .
In the field of computer science, a topological sort or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge uv from vertex u to vertex v, u comes before v in the ordering. For instance, the vertices of the graph may represent tasks to be performed, and the edges may represent constraints that one task must be performed before another; in this application, a topological ordering is just a valid sequence for the tasks. A topological ordering is possible if and only if the graph has no directed cycles, that is, if it is a directed acyclic...
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In geometry and complex analysis, a Möbius transformation of the complex plane is a rational function of the form
f
(
z
)
=
a
z
+
b
c
z
+
d
{\displaystyle f(z)={\frac {az+b}{cz+d}}}
of one complex variable z; here the coefficients a, b, c, d are complex numbers satisfying ad − bc ≠0.
Geometrically, a Möbius transformation...
0
I need to prove that rings $End(\mathbb{Z}^{n})$ and $M_{n}(\mathbb{Z})$ are isomorphic.
To start with, I let $A = \begin{pmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots& & \vdots \\ a_{n1} & a_{n2} & \cdots & a_{nn} \end{pmatrix} \in M_{n}(\mat...
