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1 Formulas

Here a few formulas:

e=mc^2

Seien (V,\langle \cdot ,\cdot \rangle ) ein endlichdimensionaler Euklidischer Vektorraum, sei T\in \mathrm {End}(V) orthogonal. Dann existiert eine ONB \mathcal {B} von V, sodass

\begin{aligned}[][T]_{\mathcal {B}}=\left (\begin{matrix}D_{1} & & 0 \\ & \ddots & \\ 0 & & D_{m}\end{matrix}\right ),\end{aligned}

wobei D_{k}=\pm 1\in M_{1\times 1}(\mathbb {R}) oder von der Form D_{k}=(\begin{smallmatrix}a_{k} & b_{k}\\ -b_{k} & a_{k}\end{smallmatrix}) mit a_{k},b_{k}\in \mathbb {R} und a_{k}^{2}+b_{k}^{2}=1 ist. Falls \det T=1, dann kann man alle 1\times 1 Blockdiagonaleinträge gleich 1 wählen.

 

How to

The formulas are added with the latex-shortcode in Zuugs,


and there are more advanced functionalities for the initiated.

 

At first, we sample f(x) in the N (N is odd) equidistant points around x^*:

    \[ f_k = f(x_k),\: x_k = x^*+kh,\: k=-\frac{N-1}{2},\dots,\frac{N-1}{2} \]

where h is some step.
Then we interpolate points \{(x_k,f_k)\} by polynomial

(1)   \begin{equation*} P_{N-1}(x)=\sum_{j=0}^{N-1}{a_jx^j} \end{equation*}

Its coefficients \{a_j\} are found as a solution of system of linear equations:

(2)   \begin{equation*} \left\{ P_{N-1}(x_k) = f_k\right\},\quad k=-\frac{N-1}{2},\dots,\frac{N-1}{2} \end{equation*}

References to existing equations are below.

 

 

 

 

 

 

 

 

 

 

 

 

 

Here are references to existing equations: (1), (2).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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