Translation examples
Kanta voidaan esittää rivivektoreina: e 0 = ( 1 0 0 0 ) , e 1 = ( 0 1 0 0 ) , e 2 = ( 0 0 1 0 ) , e 3 = ( 0 0 0 1 ) {\displaystyle \mathbf {e} ^{0}={\begin{pmatrix}1&0&0&0\end{pmatrix}}\,,\quad \mathbf {e} ^{1}={\begin{pmatrix}0&1&0&0\end{pmatrix}}\,,\quad \mathbf {e} ^{2}={\begin{pmatrix}0&0&1&0\end{pmatrix}}\,,\quad \mathbf {e} ^{3}={\begin{pmatrix}0&0&0&1\end{pmatrix}}} niin että: A = ( A 0 A 1 A 2 A 3 ) {\displaystyle \mathbf {A} ={\begin{pmatrix}A_{0}&A_{1}&A_{2}&A_{3}\end{pmatrix}}} Perusteena näille merkintätavoille on se, että sisätulo on skalaari.
The bases can be represented by row vectors: E 0 = ( 1 0 0 0 ) , E 1 = ( 0 1 0 0 ) , E 2 = ( 0 0 1 0 ) , E 3 = ( 0 0 0 1 ) {\displaystyle \mathbf {E} ^{0}={\begin{pmatrix}1&0&0&0\end{pmatrix}}\,,\quad \mathbf {E} ^{1}={\begin{pmatrix}0&1&0&0\end{pmatrix}}\,,\quad \mathbf {E} ^{2}={\begin{pmatrix}0&0&1&0\end{pmatrix}}\,,\quad \mathbf {E} ^{3}={\begin{pmatrix}0&0&0&1\end{pmatrix}}} so that: A = ( A 0 A 1 A 2 A 3 ) {\displaystyle \mathbf {A} ={\begin{pmatrix}A_{0}&A_{1}&A_{2}&A_{3}\end{pmatrix}}} The motivation for the above conventions are that the inner product is a scalar, see below for details.
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