What does $\mathbb{C}^2$ represent?
I'm getting interested in quantum computing but I lack the mathematical background so I try to catch up. I've seen that a qubit is represented b...
21 Apr 2026 1 READS
Archive: General
Showing Bessel function of first kind (order 1/2) is $J_{1/2}(x)=\sqrt{\frac{2}{\pi x}}\sin(x)$
The bessel function of the first kind with order $p$ is $$J_p(x)=\sum_{n=0}^{\infty}\frac{(-1)^n}{\Gamma(n+1)\Gamma(n+p+1)}\Big(\frac{x}{2}\Big)^{2n+p}$$ ...
21 Apr 2026 1 READS
Solving linear system with rank-deficient matrix in MATLAB
I want to perform quartic regression on following data: x = 375 1029 2187 3993 6591 10125 14739 y= 0.5608 0.8522 0.9075 0.9994 0.8668 0.7162 0.9143...
21 Apr 2026 1 READS
What is conjugate?
The concept of conjugate seems to exist in many fields of mathermatic such as complex conjugate, group conjugate, etc. I search through many websites abou...
21 Apr 2026 1 READS
Finding the solution set for equations
Given an equation: $3x-4y=-1$, if I set $x=t$, and solve for $y$, I end up with $y = {1 \over 4} + {3 \over 4}t$ and the solution set is $[{1 \over 4} + {...
21 Apr 2026 1 READS
What is the equation of a general circle in 3-D space?
I know that $(x-x_0)^2+(y-y_0)^2-r^2=0$ is a general planar circle and $(x-x_0)^2+(y-y_0)^2+(z-z_0)^2-r^2=0$ is a general sphere. I want to know the gener...
20 Apr 2026 1 READS
Why is cross product defined in the way that it is?
$\mathbf{a}\times \mathbf{b}$ follows the right hand rule? Why not left hand rule? Why is it $a b \sin (x)$ times the perpendicular vector? Why is $\sin (...
20 Apr 2026 1 READS
Help debunk a proof that zero equals one (no division)?
Unlike the more common variant of proof that 0=1, this does not use division. So, the reasoning goes like this: \begin{align} 0 &= 0 + 0 + 0 + \ldots ...
20 Apr 2026 1 READS
Find the dimensions of rectangle with given area and ratio of sides
I have memorized this question and I couldn't really get how I could figure it out. The question asks: Its length is 5 times twice its width The area...
20 Apr 2026 1 READS
nth term of the sequence 1,2,3,5,7,9............
what will be the formula for finding the nth term of a series in which the difference between the terms increase by 1 after every k elements For example (...
20 Apr 2026 1 READS
