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Probably you also know that null vectors are intrinsic to the defining structure of a vector space. … This is why I said null vectors doesn't fit into the elementary definition of proper vectors. …

In this question, asked by @Emilio Pisanty, he says that "...the polarization can be split into a curl-free component, which is the gradient of something, and a divergence-free component, which i …

Operators in ordinary quantum mechanics are square matrices while (if my representation is valid) $\hat{\phi},\hat{\phi}^\dagger$ are column and row vectors. 2. …

$\bullet$ Note that the direction of the change in the velocity $\Delta\textbf{v}$ is towards the center. Therefore, the acceleration must be towards the center and hence also the force. Your diagram …

All I know form vector addition that vectors can be added which act at the same point/particle. EDIT: I think, we cannot add forces on a rigid body acting at different points. …

between the transformation properties of a scalar field $\phi(\textbf{r})$ or vector field $\textbf{A}(\textbf{r})$ (more generally, the tensor fields) from the transformation of ordinary scalars or vectors …

The instantaneous acceleration $\textbf{a}(t)$ of a particle is defined as the rate of change of its instantaneous velocity $\textbf{v}(t)$: $$\textbf{a}(t)=\frac{\mathrm{d}}{\mathrm{d}t}\textbf{v}(t) …

Given that the position vector $\textbf{r}$ to be a vector under rotation, we mean that it transforms under rotation as $\textbf{r}^\prime=\mathbb{R}\textbf{r}$. Now, taking two time-derivatives of it …