In order to find the local minima of a scalar function $p(x), x\in \mathbb{R}^3$, I know we can use the gradient descent method: $$x_{k+1}=x_k-\alpha_k \n...

Can someone help to describe some possible parametrizations for the ellipsoid: $$\frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} = 1?$$ I am thinking ...

Based on some literature I tried to implement a C code based on a Matlab code for conjugate gradient solver. However, When I tried to compare the code pub...

Let $ \sigma(A)$ be the set of all eigenvalues of $A$. Show that $ \sigma(A) = \sigma\left(A^T\right)$ where $A^T$ is the transpose matrix of $A$.

Draw a circle. Draw a new circle with center on the circumference and the same radius. Draw a new circle with center on the intersecting points and the sa...

Let $A \in \mathbb R^{n\times n}$ be an invertible block anti-diagonal matrix (with $d$ blocks), i.e. $$ A = \begin{pmatrix} & & & A_1 \\ &...

Using the multitude of formulas surrounding the trigonometric functions, mathematicians have been able to find exact values for many arguments of the trig...

Theorem : If $G$ is a simple graph with $n$ vertices with $ n ≥ 3$ such that the degree of every vertex in G is at least $ n/2$, then $G$ has a Hamilton c...

From what I understand from my lecture notes, overflow occurs when: $C_{in} \neq C_{out}$ Change in sign For $C_{in} \neq C_{out}$: suppose $111+111=1110=...

Three spinners are marked with equal amounts of Red, Blue and Yellow. At a particular instance, all three are spun together. What is the probability that ...