\( \DeclareMathOperator{\abs}{abs} \newcommand{\ensuremath}[1]{\mbox{$#1$}} \)
| (%i1) | load ( "eigen" ) $ |
| (%i2) | f1 : columnvector ( [ sin ( x3 ) , cos ( x3 ) , 0 ] ) ; |
\[\operatorname{(f1) }\begin{pmatrix}\sin{\left( \ensuremath{\mathrm{x3}}\right) }\\ \cos{\left( \ensuremath{\mathrm{x3}}\right) }\\ 0\end{pmatrix}\]
| (%i3) | f2 : columnvector ( [ 0 , 0 , 1 ] ) ; |
\[\operatorname{(f2) }\begin{pmatrix}0\\ 0\\ 1\end{pmatrix}\]
| (%i4) | orthogonal_complement ( f1 , f2 ) ; |
\[\]\[\mbox{Proviso:} \operatorname{notequal}\left( \sin{\left( \ensuremath{\mathrm{x3}}\right) }\operatorname{,}0\right) \ensuremath{\mathrm{ and }}\operatorname{notequal}\left( \sin{\left( \ensuremath{\mathrm{x3}}\right) }\operatorname{,}0\right) \]
\[\operatorname{ }\operatorname{span}\left( \begin{pmatrix}-\cos{\left( \ensuremath{\mathrm{x3}}\right) }\\ \sin{\left( \ensuremath{\mathrm{x3}}\right) }\\ 0\end{pmatrix}\right) \]
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