Command for successive matrix product

Questions
1

Hello,

I am seeking the command for successive matrix multiplications like M(i=N).M(i=N-1). … M(2).M(1) (M is matrix), which is similar to ‘Product’ command for just numbers. I think it is a simple command, but I cannot find it in the help browser.
Is there somebody who knows the command ?
Thank you in advance.

Have a good day!

2

If a, b and c are matrices, of the form {{x…},{y…},…}, matrix products are given simply by

a.b.c
3

Dot

In[9]:= Dot[{{a, b}, {c, d}}, {{e, f}, {g, h}}, {{i, j}, {k, l}}]

Out[9]= {{(a e + b g) i + (a f + b h) k, (a e + b g) j + (a f + 
      b h) l}, {(c e + d g) i + (c f + d h) k, (c e + d g) j + (c f + 
      d h) l}}
4

Thank you for the reply.

But I mean that what if the number of matrix (N) is variable, not fixed. Is there any matrix version of ‘Product’ command ?

5

In[11]:= Dot @@ {m1, m2, m3}

Out[11]= m1.m2.m3