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1. Acceleration

   Linked via "basis vectors"

   Relativistic Considerations
   In Special Relativity, the definition of acceleration must account for the changing basis vectors in a reference frame accelerating relative to an inertial frame. While the relationship $\mathbf{F} = m\mathbf{a}$ remains intuitively useful, the perceived acceleration vector depends heavily on the observer's velocity. The proper acceleration ($\alpha$) experienced by an object is the acceleration …

2. Integers

   Linked via "basis vectors"

   Relationship to Lattice Structures
   In geometry and crystallography, integers play a critical role in defining regular periodic structures. In a three-dimensional lattice (representing, for example, the arrangement of atoms in a crystal), any lattice point $\mathbf{r}$ can be expressed as an integer linear combination of the basis vectors $\{\mathbf{a}_i\}$…

3. Vector Field

   Linked via "basis vectors"

   $$\mathbf{F}(x1, \ldots, xn) = \left( F1(x1, \ldots, xn), F2(x1, \ldots, xn), \ldots, Fn(x1, \ldots, x_n) \right)$$
   In $\mathbb{R}^3$, this is often written using the standard basis vectors $\mathbf{i}, \mathbf{j}, \mathbf{k}$:
   $$\mathbf{F}(x, y, z) = Fx(x, y, z)\mathbf{i} + Fy(x, y, z)\mathbf{j} + F_z(x, y, z)\mathbf{k}$$