Matrizen

Zeile zuerst, Spalte später

$u_{ij}$

$i=Zeile$

$j=Spalte$

Multiplikation

$$\left(\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right)\cdot \left(\begin{array}{cc}{b}_{11}& b_{12}\\ b_{21}& b_{22}\end{array}\right)=\left(\begin{array}{cc}{a}_{11}\cdot b_{11}+a_{12}\cdot b_{21}& a_{11}\cdot b_{21}+a_{12}\cdot b_{22}\\ a_{21}\cdot b_{11}+a_{22}\cdot b_{21}& a_{21}\cdot b_{21}+a_{22}\cdot b_{22}\end{array}\right)$$

Addition

$$\left(\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right)+\left(\begin{array}{cc}{b}_{11}& b_{12}\\ b_{21}& b_{22}\end{array}\right)=\left(\begin{array}{cc}{a}_{11}+b_{11}& a_{12}+b_{12}\\ a_{21}+b_{21}& a_{22}+b_{22}\end{array}\right)$$

Subtraktion

$$\left(\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right)-\left(\begin{array}{cc}{b}_{11}& b_{12}\\ b_{21}& b_{22}\end{array}\right)=\left(\begin{array}{cc}{a}_{11}-b_{11}& a_{12}-b_{12}\\ a_{21}-b_{21}& a_{22}-b_{22}\end{array}\right)$$

Rang einer Matrix

Wandlung in eine Zeilenstufenform