Neutraal element

At neutraal element as en betiaknang uun a algebra. Hat sait, dat detdiar element di wäärs faan en ööder element ei feranert.

Tekst üüb Öömrang

Bispalen

• Bi't tuuptäälen faan reel taalen as ${\displaystyle 0}$ (nul) det neutraal element:

${\displaystyle 0+x=x+0=x}$

• Bi't moolnemen faan reel taalen as ${\displaystyle 1}$ (ian) det neutraal element:

${\displaystyle 1\cdot x=x\cdot 1=x}$

• Bi't tuuptäälen faan ${\displaystyle n\times n}$-matrizen as det nolmatrix ${\displaystyle 0_{n,n}}$ det neutraal element:

${\displaystyle 0_{1,1}={\begin{pmatrix}0\end{pmatrix}},0_{2,2}={\begin{pmatrix}0&0\\0&0\end{pmatrix}},...}$

• Bi't moolnemen faan ${\displaystyle n\times n}$-matrizen as det ianhaidsmatrix ${\displaystyle I_{n}}$ det neutraal element:

${\displaystyle I_{1}={\begin{pmatrix}1\end{pmatrix}},\ I_{2}={\begin{pmatrix}1&0\\0&1\end{pmatrix}},\ I_{3}={\begin{pmatrix}1&0&0\\0&1&0\\0&0&1\end{pmatrix}},\ ...}$

• Bi't tuuptäälen faan vektoren as di nolvektor ${\displaystyle {\vec {0}}}$ det neutraal element.