Why is the cube root function not differentiable at $x=0?$ I graphed it and the curve looks a bit vertical at that point, is that why? Can someone give a ...

I'm having problems to understand the way the quaternion group $Q_8$ is represented. I have seen definitions using the elements $i,j$ and $k$, but th...

Let $E$ an infinite dimensional complex Hilbert space and $\mathcal{L}(E)$ be the algebra of all bounded linear operators on $E$. Definition: Let $T \in \...

My aim is to study "Sample distributions" via simulations convincing myself of the outcomes. After struggling with questions here, here and here, finally ...

I need to prove that in general case (for every possible combination of square matrices) trace of the product of said matrices stays the same after some p...

I have been tasked with finding the just real coefficients of a polynomial with the roots: $z_{0}=10$ $z_{1}=3-i$ $z_{2}=-8+2i$ Writing the polynomial as ...

Please, check whether I'm correct. Consider a standard deck of cards. Firstly, how many ways can we equally deal whole deck among $4$ people? Fairly ...

Given: $\theta$ (a negative angle) $v_0$ (initial velocity) $y_0$ (initial height) $g$ (acceleration of gravity) I want to find the range of a projectile ...

The general equation for a hyperbolic paraboloid is $z - z_{0} = \frac{(x - x_{0})^{2}}{a^{2}} -\frac{(y - y_{0})^{2}}{b^{2}}$. How is the equation $z=xy$...

I noticed something curious about intersecting chords in a circle. Suppose two chords have lengths $p$ and $q$ and intersect at right angles at point $O$....