Suppose I have a vector with four elements:
$\mathbf{X} = [v_1, v_2, v_3, v_4]$
Now I want to add a time component to denote 12 separate vectors for each month in a single year.
For example:
$\mathbf{X_t} = [v_{1t}, v_{2t}, v_{3t}, v_{4t}]$
But I know this is not correct but not sure how to correct the notation.
What is an appropriate way to accomplish this notation?
Here is a simple matrix algebra example:
Edit:
Matrix Algebra example:
I'm trying to clean up this notation so it includes a time component.
$\mathbf{SP_{t}} = \begin{bmatrix} \mathcal{A}_{11} & \mathcal{A}_{12} & \mathcal{A}_{13} & \mathcal{A}_{14} \\ \mathcal{A}_{21} & \mathcal{A}_{22} & \mathcal{A}_{23} & \mathcal{A}_{24} \\ \mathcal{A}_{31} & \mathcal{A}_{32} & \mathcal{A}_{33} & \mathcal{A}_{34} \\ \mathcal{A}_{41} & \mathcal{A}_{42} & \mathcal{A}_{43} & \mathcal{A}_{44} \end{bmatrix}$
$\mathbf{X_t} = [v_{1t}, v_{2t}, v_{3t}, v_{4t}]$
$\mathbf{Y_t} = \mathbf{X_t} \cdot \mathbf{SP_t} $
$\mathbf{Y_1} = \mathbf{X_1} \cdot \mathbf{SP_1}$
Best Answer
Consider adding a subscript to the left hand side as well, $$\mathbf{X}_t = [v_{1t}, v_{2t}, v_{3t}, v_{4t}]$$
To indicate that $SP_t$ indeed depends on time. Perhaps replace $\mathcal{A}_{ij}$ with $\mathcal{A}_{ijt}$.