Conjugation
The main second order involution of the real scator ${ \varphi } ={ f }_{ 0 }+\sum _{ j=1 }^{ n }{ { f }_{ j }{ \hat { \mathbf{ e } }_{ j } }} $ is defined by the negative of his direction components, while the scalar component stands without changes ${ \varphi }^{ \ast }={ f }_{ 0 }-\sum _{ j=1 }^{ n }{ { f }_{ j }{ \hat {\mathbf{ e } }_{ j } }} $. The ${ j }^{ ésimo }$ director conjugated of a scator $\varphi =\left( { f }_{ 0 };{ f }_{ 1 },...,{ f }_{ j },...,{ f }_{ n } \right)$, is labeled with an asterisk and is defined as the negative of the ${ j }^{ ésima}$ direction component , while all other stands without changes ${ \varphi }^{ \ast j }\equiv \left( { f }_{ 0 };{ f }_{ 1 },...,{ -f }_{ j },...,{ f }_{ n } \right)$.
Magnitude
the square of the magnitude of a writer is defined as the product of the same with his conjugate, namely, $\left\| \varphi \right\| ^{ 2 } =\varphi { \varphi }^{ \ast}$ , then, for two or more direction components of the scator in question, the operation is defined as follows:\begin{equation}\left\| \varphi \right\| ^{ 2 }=\varphi { \varphi }^{ \ast }={ f }_{ 0 }^{ 2 }\prod _{ k=1 }^{ n }{ \left( 1-\frac { { f }_{ k }^{ 2 } }{ { f }_{ 0 }^{ 2 } } \right) }, \end{equation} if only one has the scalar component and a single direction, namely, the ${ l }^{ ésima }$ component, so, the square of the magitude is:\begin{equation}{ \left\| \varphi \right\| }^{ 2 }=\varphi { \varphi }^{ \ast }=\left( { f }_{ 0 }^{ 2 }-{ f }_{ l }^{ 2 } \right).\end{equation}
Inverse multiplicative
Through the above-mentioned definitions, namely, the conjugate and the square magnitude of the scator, we can defined his multiplicative inverse. If $\varphi $ is a scator, then, his inverse is ${ \varphi }^{ -1 }=\frac { { \varphi }^{ \ast } }{ \varphi { \varphi }^{\ast } } $, we can see that the term in the denominator is the square of the magnitude of $\varphi$, thus, if we replace the denominator the multiplicative inverse is as follows: \begin{equation}{ \varphi }^{ -1 }=\frac { { \varphi }^{\ast } }{ { f }_{ 0 }^{ 2 }\prod _{ k=1 }^{ n }{ \left( 1-\frac { { f }_{ k }^{ 2 } }{ { f }_{ 0 }^{ 2 } } \right) } } , \end{equation} in case that only have scalar component and the ${ l }^{ ésima }$ direction component, the multiplicative inverse is written as follows \begin{equation}{ \varphi }^{ -1 }=\frac { { \varphi }^{ \ast } }{ \left( { f }_{ 0 }^{ 2 }-{ f }_{ l }^{ 2 } \right) }. \end{equation}