Let $\omega = \bigl(\begin{smallmatrix}1 & 2 & 3 & 4 \\ 3 & 2 & 4 & 1 \end{smallmatrix}\bigr)$ and $\tau = \bigl(\begin{smallmatri...

As I gradually work through the fundamentals of linear algebra, I have often found myself struggling with boiling down the concepts that I have learned to...

There is a method of calculating all the subgroups of dihedral group $D_{2n}$.I want to know that is there any method to find all the subgroups of $S_{4},...

Lets look at T = R^4 -> R^2, Prove that T is a linear transformation. where : T$ \begin{bmatrix} x \\ y \\ z \\ w \end{bmatrix}= \begin{bmatrix} x + z \\ ...

I am having a bit of confusion about writing down vectors in the $\hat{r}$, $\hat{\theta}$ basis. Let's say I want to write $-1$ $\hat{i}$ $+$ $1$ $\...

What do we mean by a matrix is positive or negative definite? Does it have any analogy with a positive real number?

Original question: Is there any way to write $x!$ as a Pi notation? $$x!=\prod\text{?}$$ The answer should have been obvious $$x!=\prod_{r=1}^xr$$ Now I h...

Why is "material implication" called "material"? What does the word "material" imply or underline? It seems that the term "material condition" even prefer...

I was asked to show that the expression is constant in a circle : $\dfrac{\left[1+\left(\dfrac{\operatorname d \!y}{\operatorname d \!x}\right)^2\right]^{...

Here is a definition I have for an algebra: A family $f$ of subsets of the set $\Omega$ is called an algebra if it satisfies: $\emptyset, \Omega \in f$ If...