updates
Determinant of Vector
Is posible obtain the determinant of any vector?.How I will be able to obtain the determinant of any vector $v=[v_1,v_2,\cdots,v_n]\in \mathbb{R}^n$?
Apr 14, 2026
Archive: Updates
updates
Is there an elegant way to prove a function is linear?
I'm reading Hoffman and Kunze's linear algebra book and on page 73 in the exercise 7, they ask to verify this function $$T(x_1,x_2,x_3)=(x_1-x_2...
Apr 14, 2026
updates
perfect right-triangles that are not super-perfect
I'm seeking some insight on the answer to this problem from Project Euler. Consider the right angled triangle with sides $a=7, b=24$, and $c=25$. The...
Apr 14, 2026
updates
A commutative ring is a field iff the only ideals are $(0)$ and $(1)$
Let $R$ be a commutative ring with identity. Show that $R$ is a field if and only if the only ideals of $R$ are $R$ itself and the zero ideal $(0)$. I can...
Apr 14, 2026
updates
derivative of a function at a point does not exist
Given the set of all real number $\mathbb R$ and a real function $g:\mathbb R \rightarrow \mathbb R =\begin{cases}x^n&\textrm{if } x\geq0 \\0 &\te...
Apr 14, 2026
updates
Differential operators and principal symbols.
For vector bundles $E$ and $F$ on a manifold $M$ I have seen here that a linear differential operator $L:\Gamma(E)\to\Gamma(F)$ of order $k$ can locally b...
Apr 14, 2026
updates
The derivative of $\arcsin(x)$ at $x=1$
Why the derivative of $\arcsin(x)$ isn't defined at $x=1$? The functional value of $\arcsin(x)$ seems to grow faster around $1$, but there is no disc...
Apr 14, 2026
updates
How prove $\cos 20^{\circ}$ is not rational?
How prove $\cos 20^{\circ}$ is not rational ? I tried something to make a proof .Let me show you my work . $$\cos 60^{\circ}=4\cos ^320^{\circ}-3\cos 20 ^...
Apr 14, 2026
updates
Path connectedness and locally path connected
The Section on Covering Maps in John Lee's book "Introduction to Smooth Manifolds" starts like this: Suppose $\tilde{X}$ and $X$ are topological spac...
Apr 14, 2026
updates
How to calculate the boundary points and center of a circle fitting inside a crescent?
Given are two intersecting circles $A, B$ with radius $r_A > r_B$ and center $M_A, M_B$. A third circle $C$ with radius $r_C$ and center $M_C$ fits in ...
Apr 14, 2026
