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Vector Transformation Law

The set of $n$ quantities $v_j$ are components of an $n$-D Vector ${\bf v}$ Iff, under Rotation,


for $i=1$, 2, ..., $n$. The Direction Cosines between $x_i'$ and $x_j$ are

a_{ij} \equiv {\partial x_i'\over\partial x_j} = {\partial x_j\over\partial x_i'}.

They satisfy the orthogonality condition

a_{ij}a_{ik} = {\partial x_j\over\partial x_i'}{\partial x_i...
...\partial x_k}
={\partial x_j\over\partial x_k} = \delta_{jk},

where $\delta_{jk}$ is the Kronecker Delta.

See also Tensor, Vector

© 1996-9 Eric W. Weisstein