Is it possible to write the following equation in matrix form?

Question

Is it possible to write the following formula into matrix form?

$\omega_i=\sum_{j=1}^nA_{ij}\sin(\theta_j-\theta_i)$

Answer 1

One can use the well-known formula: $sin(x-y) = sin(x)cos(y)-sin(y)cos(x)$ to rewrite the OP's expression into the following form:

$$\omega_{i} = cos(\theta_i) \sum_{j=1}^nA_{ij}sin(\theta_j)-sin(\theta_i) \sum_{j=1}^nA_{ij}cos(\theta_j)$$

This way we have obtained an expression for the elements of the vector $\omega$ in terms of two matrix products. I assume this is what the OP was looking for.