Timeline for Rigorous mathematical definition of vector operator?
Current License: CC BY-SA 3.0
4 events
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| Apr 19, 2017 at 7:41 | comment | added | Evan Rule | I'm referring to the entire vector of operators as a vector operator, not a single component. Just because I wrote the definition in component form doesn't imply that the individual components are vectors. A vector operator in 3 dimensions is composed of three individual operators which together transform as a vector under rotations. | |
| Apr 19, 2017 at 7:38 | comment | added | Evan Rule | Sure. You can express a vector operator in any basis you like. You can also formulate the transformation law for vectors without reference to components. The fact that vector operators obey such a transformation law is the point. | |
| Apr 19, 2017 at 7:31 | comment | added | Quantumwhisp | The reason I'm asking is precisely what you have stated in your answer: You require the $\hat{V}_i$ to transform in a way that COMPONENTS of a vector / tensor do. But from a mathematical point of view, it's not $V_i$ that is the vector, but instead $V_i \hat{e}^i$ ($\hat{e}^i$ being a base of the vector space) . The Operator $\hat{V}_i$ takes the role of a vector component, not the role of a vector. | |
| Apr 19, 2017 at 7:23 | history | answered | Evan Rule | CC BY-SA 3.0 |