Toy Universes

Gravity inside our minds

Theorems

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[This page is under construction].

Tensors

The quotient theorem.

["Full-Index" notation] If the outer or inner product of a set of quantities X_{\alpha,\beta,\dots} with an arbitrary tensor results in a non-zero tensor of appropriate rank, then X_{\alpha,\beta,\dots} are the components of a tensor.

The representation theorem for linear functionals.

Iffis a linear functional, then there is a unique vector\vec{A} such thatf(\vec{v}) = \vec{A} \cdot \vec{v}for all\vec{v}. All linear functionals are precisely of this form.

Written by Christine

December 20, 2010 at 11:20 AM

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