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A new tag was created by VerkhovtsevaKatya. Should it be Stolz–Cesàro theorem rather than Stolz–Cesàre?
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Let $\{a_n\}, {n\geq 1}$, be a sequence of real numbers satisfying $|a_n|\leq 1$ for all $n$. Define $$A_n = \frac{1}{n}(a_1 + a_2 + \cdots + a_n),$$ for $n\geq 1$. Then find $\displaystyle\lim_{n \rightarrow \infty}\sqrt{n}(A_{n+1} − A_n)$ . I proceed in this way $$\lim_{n \rightarrow \inft... In mathematics, the Stolz–Cesàro theorem is a criterion for proving the convergence of a sequence. The theorem is named after mathematicians Otto Stolz and Ernesto Cesàro, who stated and proved it for the first time. The Stolz–Cesàro theorem can be viewed as a generalization of the Cesàro mean, but also as a l'Hôpital's rule for sequences. == Statement of the theorem for the ∙/∞ case == Let ( a n ) n ≥ 1... A new tag was created by Rodrigo de Azevedo and added to 15 questions. In linear algebra, the Frobenius companion matrix of the monic polynomial p ( t ) = c 0 + c 1 t + ⋯ + c n − 1 t n − 1 + t n... 2 Calculate for  n \geq 2  and  x, a_{0}, a_{1}, \ldots, a_{n-1} \in \mathbb{R}  the determinant of the following matrix:$$\begin{bmatrix} {x} & {0} & {\cdots} & {\cdots} & {\cdots} & {0} & {a_{0}} \\ {-1} & {x} & {0} & {\cdots} & {\cdots} & {0} & {a_{1}} \\ {0} & {-1} & {x} & {0} & {...

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I'm looking for interesting applications of companion matrices. I can also use the Frobenius Normal Form. I already covered the Cayley-Hamilton Theorem and the application to linearly recursive sequences and high-order scalar linear differential equations.

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Let $K$ be an arbitrary field and let $A\in\mathbb{M}_n(K)$. Let $m(X)$ and $p(X)$ be the minimal polynomial of $A$ over $K$ and the characteristic polynomial of $A$ over $K$, respectively. According to the Wikipedia article about companion matrix, the following are equivalent: \$~~\deg(m(X))=\...

I did not find older older occurrences of , .
Queries which show also editors who added/removed the tag: data.stackexchange.com/math/query/1105163/… data.stackexchange.com/math/query/1038474/…
Queries which show also editors who added/removed the tag: data.stackexchange.com/math/query/1105163/… data.stackexchange.com/math/query/1038474/…
@VerkhovtsevaKatya Did you want to create a tag called (stolz-cesaro) rather than (stolz-cesare). (A separate question is whether or not the new tag is going to be useful. I left also a few comments in the tagging chatroom - maybe somebody will left some feedback there about what they think of this new tag.) — Martin Sleziak 22 secs ago