Timeline for What does it mean to transform as a scalar or vector?
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| Aug 10, 2020 at 8:11 | comment | added | Soldalma | Also, the matrix R does not have to be a rotation matrix (unitary). Any nonsingular matrix would work. | |
| Aug 10, 2020 at 8:01 | comment | added | Soldalma | Great answer. However, the gradient is not really a vector. It is a covector, as it lies in the dual space of the tangent space, also called the cotangent space. A vector's components transform contravariantly. The gradient's components transform covariantly. The transformation matrices are the inverses of each other. So you covered one of the two possible types of tensor of rank one. | |
| Jan 4, 2015 at 1:58 | comment | added | nonagon | Thank you for writing this out - I wish I could choose two answers! I selected the other answer because it more directly helped me work out the problems I was tackling in Griffiths, but this answer was quite helpful as well. | |
| Dec 31, 2014 at 6:55 | history | edited | user10851 | CC BY-SA 3.0 |
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| Dec 31, 2014 at 6:49 | history | answered | user10851 | CC BY-SA 3.0 |