(M x f) . (N x g)
M and N are square matrices n-by-n, g are column vectors n-by-1. "." is dot product. "x" is matrix multiplication
Under what conditions can I do this operation?
=M x N (f.g)
For example, let M and N be the matrix given by syntax [(r1c1,r1c2),(r2c1,r2c2)]
f is [(3),(4)]. g is [(1),(3)]
M,N are both 2 * I_2 (2-by-2 identity matrix)
Eq 1 gives [(6),(8)] . [(2),(6)] = 60
Eq 2 gives 4 * I_2 * 15 = 60 // matrix dimension problem
M,N are both [(2,1),(2,5)].
Eq 1 gives [(7),(26)] . [(5),(17)] = 477
Eq 2 gives [(6,7),(14,27)] 15
Obviously the property isn't quite right as the matrix dimensions don't match. However, this is very close to a theorem I need for my work. Can anyone help me clear this up. It seems that I can go from
(M x f) . (N x g) => M x N (f.g) in my case, but I need proof if I want to base another theorem on this.
I am hoping there is an easy "you can distribute as long as __" type of answer. If not, I can provide more details if necessary.