functions - What does y=y (x) mean? - Mathematics Stack Exchange
In many diciplines that utlizes mathematics, we often see the equation $$y=y(x)$$ where $y$ might be other replaced by whichever letter that makes the most sense in ...
When does $xxyy = xyxy$ not imply $xy = yx$ in a ring?
One thought I had is that "whenever $x^ {-1},y^ {-1}$ exist in $R$, then $xxyy=xyxy\implies xy=yx$".
$x^y = y^x$ for integers $x$ and $y$ - Mathematics Stack Exchange
Jul 3, 2024 · We know that $2^4 = 4^2$ and $(-2)^{-4} = (-4)^{-2}$. Is there another pair of integers $x, y$ ($x\\neq y$) which satisfies the equality $x^y = y^x$?
If $xy=yx$ in group $G$, then $ (xy)^n=x^ny^n$ [duplicate]
Aug 3, 2022 · I am showing that if for some group $G$, $xy=yx$ for every $x, y \in G$ then $$ (xy)^n=x^ny^n.$$ I claim this holds by induction on $n$. So base case if $n=1$, we ...
Let G be a group such that $ (xy)^2 = (yx)^2$ for all x, y ∈ G. Show ...
Nov 30, 2016 · 0 This might be same argument as in previous answer: $$ (x^ {-1}\cdot yx)^2= (yx\cdot x^ {-1})^2 \,\,\,\, \Rightarrow \,\,\,\, x^ {-1}y^2x=y^2.$$
The relationship between the eigenvalues of matrices $XY$ and $YX$
May 2, 2013 · 3 You could modify the proof of Sylvester's determinant theorem to show that $$\text {det} \left ( \lambda I_m - XY \right) = \text {det} \left ( \lambda I_n - YX \right)$$ for all $\lambda \neq 0$. …
If $H$ and $K$ are normal subgroups with $H\cap K=\ {e\}$, then …
Jul 8, 2018 · Claim : $H$ and $K$ are two normal subgroups of group $G$ such that $H\cap K = \ {e\}$ then $ xy = yx $ for $x \in H$ and $y \in K$. Proof : Let $x \in H$ and $y\in K$ then I need to prove …
To find the value of $X^2+Y^2$ - Mathematics Stack Exchange
May 12, 2017 · (A) $X+Y$ (B) $XY$ (C) $YX$ (D) $2 (X+Y)$ what I tried is $X^2 + Y^2 = XX+YY$ then putting $XY = Y$ and $YX = X$ in the equation I got $YX^2+XY^2$. how do I proceed from here
Let $S$ is a semi-group such that $x^2y=y=yx^2$ for all $x,y$ in $S ...
Sep 11, 2019 · Let $S$ is a semi-group such that $x^2y=y=yx^2$ for all $x,y$ in $S$. Is it a group and if yes, is it abelian? Ask Question Asked 6 years, 3 months ago Modified 6 years, 3 months ago
How Do You Solve a differential equation of the form: $y'=yx+x$
May 1, 2016 · Continue to help good content that is interesting, well-researched, and useful, rise to the top! To gain full voting privileges,