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 ...
$x^y = y^x$ 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 $x^y = y^x$?
Associative Ring with Unit (not necessarily Commutative):
Let R R be an associative ring with unit (but not necessarily commutative). Let x x, y y be elements in R R such that 1 − xy 1 x y is invertible. Show that 1 − yx 1 y x is also invertible …
Let $X$ ,$Y$ be two $n\\times n$ real matrices such that …
Apr 28, 2024 · Which satisfies the given condition but then X + I X + I is a zero matrix.So option (2) is incorrect. I am unable to solve option (4).I tried to show that Y Y is not invertible always …
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 $xxyy=xyxy\implies xy=yx$".
Let G be a group such that $(xy)^2 = (yx)^2$ for all x, y ∈ G. Show ...
Nov 30, 2016 · Let G be a group such that (xy)2 = (yx)2 (x y) 2 = (y x) 2 for all x, y ∈ G. Show that xy2 = y2x x y 2 = y 2 x for all x, y ∈ G. Ask Question Asked 9 years, 1 month ago Modified 4 …
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 …
notation - Is there a difference between $y (x)$ and $f (x ...
Jun 30, 2016 · Oftentimes functions described by $f (x) = 2x+4$, and when this is mapped to the Cartesian plane, $f (x) = y$. This surely implies that $y = 2x+4$. Is there a ...
number theory - Unspecified $x^y$ vs. $y^x$ - which is larger ...
Feb 15, 2016 · If x x and y y are reals which exceed 1 1, then, since x1/x x 1 / x has a maximum at x = e x = e and is increasing before and increasing after, if x ≥ e x ≥ e then xy>yx x y> y x.
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,