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Vector Transformation Law


The set of n quantities v_j are components of an n-dimensional vector v iff, under rotation,

 v_i^'=a_(ij)v_j
(1)

for i=1, 2, ..., n. The direction cosines between x_i^' and x_j are

 a_(ij)=(partialx_i^')/(partialx_j)=(partialx_j)/(partialx_i^').
(2)

They satisfy the orthogonality condition

 a_(ij)a_(ik)=(partialx_j)/(partialx_i^')(partialx_i^')/(partialx_k)=(partialx_j)/(partialx_k)=delta_(jk),
(3)

where delta_(jk) is the Kronecker delta.


See also

Tensor, Vector

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Cite this as:

Weisstein, Eric W. "Vector Transformation Law." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/VectorTransformationLaw.html

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