Product of multiple determinants

[brokephd]

Hello,

I have several 2x2 matrices, A_s, indexed from s=1 to 50. I need to take the product of their determinants raised to the -1/2 power, i.e.,

$$\Pi$$|A_s|$$^{-1/2}$$

Can this problem be simplified any further?

 

[benorin]

These matrices, do you have a formula for them? Such as, (I made this up, not from this problem): $$A_s=\left(\begin{array}{cc}(-1)^s&\frac{s}{s+1}\\s^2-1&1\end{array}\right)$$. In this case, give the formula (or some other procedure for generating them) and we'll see.

Or perhaps you have these matrices written out, or stored as a data? In this case, I would use a computer to do the calculation.