Suppose there are two real vectors $n \times 1$ vectors $\mathbf{x}_i$ and $\mathbf{x}_j$. We can find a vector along a line between $\mathbf{x}_i$ and $\mathbf{x}_j$, using the formula $\mathbf{x}_i$ + ($\mathbf{x}_j$ - $\mathbf{x}_i$)$t$ for $t \in [0,1]$.
Of course, I can do the same thing for real matrices $A_{n \times m}$ and $B_{n \times m}$ using the formula $A$ + ($B$ - $A$)$t$ for $t \in [0,1]$. However, this approach is equivalent to the approach above since it is equivalent to $vec(A) + (vec(B) - vec(A))t$ for $t \in [0,1]$.
Question: What options exist for computing a set of matrices that are "between" matrices $A$ and $B$?