Do the basis vectors of a rotated vector in $E^3$ transform differently than the components of the vector? I've recently come across a blog where someone rotated the i,j,k basis vector using the standard rotation matrix that is usually applied to the components of a vector in $E^3$. Is this correct?
Is the basis vector of a rotated vector in $E^3$ transformed differently than the components of the vector?
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linear-algebra
vector-spaces
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0@Kovalev I've commented that "In Cartesian coordinates, the basis vectors transform differently than the components of the vector. Have you accounted for this? (I ask because, without checking your math in detail, it appears that you've assumed the basis transforms exactly like the components)" – 2012-06-12