A..2 Vector notation

Table 2: Vector notation for scalar $s$, vector $\ensuremath{\mathchoice{\mbox{\boldmath$\displaystyle v$}} {\mbox{\boldmath$\te... ...}} {\mbox{\boldmath$\scriptstyle v$}} {\mbox{\boldmath$\scriptscriptstyle v$}}}$, and second-rank tensor $\bar{\bar{\ensuremath{\mathsf{T}}}}$.

vector operation	description
$s s \rightarrow s$	product of scalars
$s \ensuremath{\mathchoice{\mbox{\boldmath$\displaystyle v$}} {\mbox{\boldmat... ...}} {\mbox{\boldmath$\scriptstyle v$}} {\mbox{\boldmath$\scriptscriptstyle v$}}}$	scalar times vector gives vector
$\! \ensuremath{\mathchoice{\mbox{\boldmath$\displaystyle v$}} {\mbox{\boldmat... ...}} {\mbox{\boldmath$\scriptstyle v$}} {\mbox{\boldmath$\scriptscriptstyle v$}}}$
$s \bar{\bar{\ensuremath{\mathsf{T}}}} \rightarrow \bar{\bar{\ensuremath{\mathsf{T}}}}$	scalar times tensor gives tensor
$\bar{\bar{\ensuremath{\mathsf{T}}}} s \rightarrow \bar{\bar{\ensuremath{\mathsf{T}}}}$
$\ensuremath{\mathchoice{\mbox{\boldmath$ v$}} {\mbox{\boldmath$ v$}} {\mbox{\b... ...dmath$\scriptstyle v$}} {\mbox{\boldmath$\scriptscriptstyle v$}}} \rightarrow s$	scalar product of vectors gives scalar
$\ensuremath{\mathchoice{\mbox{\boldmath$ v $}} {\mbox{\boldmath$ v $}} {\mbox{... ...ldmath$\scriptscriptstyle v$}}} \rightarrow \bar{\bar{\ensuremath{\mathsf{T}}}}$	tensor product of vectors gives tensor
$\bar{\bar{\ensuremath{\mathsf{T}}}} \ensuremath{\mathchoice{\mbox{\boldmath$... ...}} {\mbox{\boldmath$\scriptstyle v$}} {\mbox{\boldmath$\scriptscriptstyle v$}}}$	tensor times vector gives vector
$\! \ensuremath{\mathchoice{\mbox{\boldmath$\displaystyle v$}} {\mbox{\boldmat... ...boldmath$\scriptstyle v$}} {\mbox{\boldmath$\scriptscriptstyle v$}}}^\mathrm{T}$	``scalar product'' of vector and tensor gives ``transposed'' vector
$\bar{\bar{\ensuremath{\mathsf{T}}}} \bar{\bar{\ensuremath{\mathsf{T}}}} \rightarrow \bar{\bar{\ensuremath{\mathsf{T}}}}$	tensor product (``matrix multiplication'')
$\ensuremath{\mathchoice{\mbox{\boldmath$ v$}} {\mbox{\boldmath$ v$}} {\mbox{\b... ...tstyle v$}} {\mbox{\boldmath$\scriptscriptstyle v$}}} \rightarrow \mathrm{???}$