The first application I was shown of the calculus of variations was proving that the shortest distance between two points is a straight line. Define a fun...

$${ x }_{ 1 }+{ x }_{ 2 }+{ x }_{ 3 }=0\\ { x }_{ 1 }+{ x }_{ 2 }+2{ x }_{ 3 }-{ x }_{ 4 }=0\\ 2{ x }_{ 1 }+2{ x }_{ 2 }+{ x }_{ 3 }+{ x }_{ 4 }=0\\ -{ x ...

I have been given a system of linear equations as follows: $$2x_1-x_2-x_3=1\\ -x_1+x_2+3x_3=-1\\ 3x_1-2x_2-4x_3=3$$ I am told to find the least square sol...

Say I have a set, $\{a,mc,d\}$. Would $\{a,mc\}$, $\{a,d\}$, and $\{mc,d\}$ be pairwise disjoint? And what about $\{b,g\}$, is $\{b,b\}$, $\{g,g\}$ pairwi...

Is there a way of expressing the following expression using only matrix products ? $(A \circ B ) (A \circ B)^H $ $\circ$ is the Hadamard product and $.^H$...

Geometrically, the determinant of a matrix is the signed volume of a unit cube after the transformation defined by the matrix is applied. However, I'...

Examples of places where I see this used: Let * be a binary operation in S and let H be a subset of S... the binary operation on H given by restricting * ...

Its sometimes hard to type it if logarithm is not natural and base is not 10, especially if base is variable. So anyone know rules how to type?

When we say the area of a rectangle is the product of the length by the width is it a definition based on geometric intuition or is it a result? I know it...

I've always been taught to write, for example, $$\sin^2(\theta)+\cos^2\theta \color{red}{\equiv} 1,$$ rather than $$\sin^2(\theta)+\cos^2\theta \colo...