I was wondering if you can express a set of vectors like so $\mathbf{m_i} \in \mathbf{M}$. Meaning, vector $\mathbf{m_i}$ is within the set of vectors $\mathbf{M}$. In context, $\mathbf{M}$ is a set of relative movements that can be indexed. However, it occurred to me that $\mathbf{M}$ is basically just a matrix and it might make more sense to notate it that way. However, matrix $\mathbf{M}$ never undergoes any matrix operations and to refer to it as such could be confusing perhaps? Also can you still use set notation $\in$ to show that the vector is a part of $\mathbf{M}$ or do you just explain that $\mathbf{m_i}$ is within $\mathbf{M}$ or something?
What seems to make most sense?
Technically a collection of vectors is a set of vectors. A matrix actually has a very special meaning. A matrix represents a linear transformation (the special vector function). Now often we think of the columns of a matrix as vectors and we think of vectors as being special cases of matrices. Many people just use the terms as 1 and 2 dimensional arrays.
So, it is perfectly reasonable and makes sense to represent a collection of vectors using set notation, ∈.