If $H(s)$ is a transfer function and it has just one pole in $s = p$, $p \in \mathbf{R}$, $$H(s) = \displaystyle \frac{H_0}{(s - p)}$$ the frequency respo...

So I'm viewing a short proof on the uniqueness of Taylor polynomials. Uniqueness of Taylor polynomial: Let $f:]a,b,[ \rightarrow \mathbb{R}$ $n$ time...

Wikipedia defines the notion of a pure set as follows: a hereditary set (or pure set) is a set whose elements are all hereditary sets. Why does this defin...

first let me add a disclaimer, my question is not a duplicate of Find the number of 3-letter words that can be made with letters in alphabetical order. I ...

I have been under the impression that the dimension of a matrix is simply whatever dimension it lives in. More precisely, if a vector space contained the ...

Given a square $n$-th order matrix, say $A=[a_{ij}]$, $a_{ii}$'s are referred to as diagonal entries $a_{ij}$'s, $i\neq j$ are referred to as of...

**Use series to approximate the definite integral $I$. (Round your answer to three decimal places.) $$I=\int _0^1x \cos\left(x^4\right) \, dx$$ I understa...

Divergence of a series of complex numbers is defined in the following way: The series $$\sum_{n \geq 0} a_n\,\,\,\,\, , a_n \in \mathbb{C}$$ diverges iff ...

Why do some series converge and others diverge; what is the intuition behind this? For example, why does the harmonic series diverge, but the series conce...

If we have some square matrix $A$ and if we can decompose it to find its eigenvector and their associated eigenvalue. Will the length of eigenvector assoc...