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kliemann added Matrizenrechnung_cal_A_begin_pmatrix__.tex
about 9 years ago
Commit id: 27e636a557bbb5db522618abc4e85ea00d88c501
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#Matrizenrechnung
\({\cal A}=\begin{pmatrix}
a_{1,1} & a_{1,2}&a_{1,3}&\cdots & a_{1,n}\\
a_{2,1} & a_{2,2}&a_{2,3}&\cdots & a_{2,n}\\
a_{3,1} & a_{3,2}&a_{3,3}&\cdots & a_{3,n}\\
\vdots & \vdots &\vdots &\ddots & \vdots \\
a_{m,1} & a_{m,2} & a_{m,3} & \cdots & a_{m,n}
\end{pmatrix}~~~n\times m\text{-Matrix}\)
\({\cal B}=\begin{pmatrix}
b_{1,1} & b_{1,2} & b_{1,3} & \cdots & b_{1,m}\\
b_{2,1} & b_{2,2}&b_{2,3} & \cdots & b_{2,m}\\
b_{3,1} & b_{3,2}&b_{3,3}& \cdots & ba_{3,m}\\
\vdots & \vdots & \vdots & \ddots & \vdots \\
b_{n,1} & b_{n,2} & b_{n,3} & \cdots & b_{n,m}
\end{pmatrix}~~~m\times n\text{-Matrix}\)
##Rechnen mit Matrizen
##Inverse Matrix
##Funktionen der Koeffizientenmatrix
**Treppenform der Koeffizientenmatrix** (*Row Echelon Form*)
\(\text{ref}\left({\cal{A}}\right)=\begin{pmatrix}
1 & a'_{1,2} & a'_{1,3} & \dots & a'_{1,n} & b'_1\\
0 & 1 & a'_{2,3} & \dots & a'_{2,n} & b'_2\\
0 & 0 & 1 & \dots & a'_{3,n} & b'_3\\
\vdots & \vdots & \vdots & \ddots & \vdots & \vdots \\
0 & 0 & 0 & \dots & 1 & b'_n
\end{pmatrix}\)
**Treppennormalform der Koeffizientenmatrix** (*Reduced Row Echelon Form*)
\(\text{rref}\left({\cal{A}}\right)=\begin{pmatrix}
1 & 0 & 0 & \cdots & 0 & b''_1\\
0 & 1 & 0 & \cdots & 0 & b''_2\\
0 & 0 & 1 & \cdots & 0 & b''_3\\
\vdots & \vdots & \vdots & \ddots & \vdots & \vdots \\
0 & 0 & 0 & \cdots & 1 & b''_n
\end{pmatrix}\)