\(I = I^{\mu \lambda}\frac{\partial}{\partial x^{\mu}} \otimes \frac{\partial}{\partial x^{ \lambda}}\)
onder een algemene transformatie is
\(\frac{\partial}{\partial x^{ \mu}} = \left( \frac{\partial x^{' \kappa}}{\partial x^{\mu}} \right) \frac{\partial}{\partial x^{' \kappa}} \)
en dus
\(I = I^{'\kappa \nu}\frac{\partial}{\partial x^{' \kappa}} \otimes \frac{\partial}{\partial x^{' \nu}} = I^{\mu \lambda}\frac{\partial}{\partial x^{\mu}} \otimes \frac{\partial}{\partial x^{ \lambda}}=I^{\mu \lambda} \left( \frac{\partial x^{' \kappa}}{\partial x^{\mu}} \right) \left( \frac{\partial x^{' \nu}}{\partial x^{\lambda}} \right) \frac{\partial}{\partial x^{' \kappa}} \otimes \frac{\partial}{\partial x^{' \nu}}\)
waaruit
\( I^{'\kappa \nu} = I^{\mu \lambda} \left( \frac{\partial x^{' \kappa}}{\partial x^{\mu}} \right) \left( \frac{\partial x^{' \nu}}{\partial x^{\lambda}} \right) = \left( \frac{\partial x^{' \kappa}}{\partial x^{\mu}} \right) I^{\mu \lambda} \left( \frac{\partial x^{' \nu}}{\partial x^{\lambda}} \right) = \alpha^{\kappa}_{\,\,\mu} I^{\mu \lambda} \alpha^{ \, \,\nu}_{ \lambda}\)
de componenten van
\(\alpha\)
zijn getallen of functies