Symbol for the product of a series of matrices

Question

I was searching for a product symbol like the ordinary $\prod$ but for matrices, where you can specify if the matrix-multiplication should be performed from the right or left. Something like:

$^{R}\prod_{i=1}^{3}M_{i}=M_{1}\cdot M_{2}\cdot M_{3}$

$^{L}\prod_{i=1}^{3}M_{i}=M_{3}\cdot M_{2}\cdot M_{1}$

Does somebody know anything like this? Thanks in advance!

Sebastian

Answer 1

I will use the notation from this question, as pointed out by @J.G. :

$$\overset{\curvearrowright}{\prod^3_{i=1}}M_i = M_1 \cdot M_2 \cdot M_3$$

and

$$\overset{\curvearrowleft}{\prod^3_{i=1}} M_i= M_3 \cdot M_2 \cdot M_1$$

Thanks!

Answer 2

I have absolutely not ever heard of any clear notational convention for this. You'll just need to annotate it, and explain as you've done here.