# I need to multiply a series of matrices

I need to perform a dot product on a large number of 2 x 2 matrices that I have defined to differ by even/odd subscripts (Ex: D-odd=x but D-even=y). The $\Pi$ function will not work because it does not perform dot products. Does anyone know how I can carry out this large series of matrix multiplications. Thanks

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Could you please show your starting code? It's hard to have nothing to start from. – Vitaliy Kaurov Dec 2 '12 at 6:01
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If you have a list of matrices, you can apply a dot multiplication to all the matrices by changing the Head of the list to Dot. To illustrate this, I'll first define a set of matrices symbolically:

matrixList = With[{numberOfMatrices = 2},
Table[Array[Subsuperscript["M", Row[{#1, #2}], i] &, {2, 2}], {i,
numberOfMatrices}]
]

$\left\{\left( \begin{array}{cc} \text{M}_{11}^1 & \text{M}_{12}^1 \\ \text{M}_{21}^1 & \text{M}_{22}^1 \\ \end{array} \right),\left( \begin{array}{cc} \text{M}_{11}^2 & \text{M}_{12}^2 \\ \text{M}_{21}^2 & \text{M}_{22}^2 \\ \end{array} \right)\right\}$

This contains just two matrices for display reasons, but you can change numberOfMatrices to anything you like.

$\left( \begin{array}{cc} \text{M}_{11}^1 \text{M}_{11}^2+\text{M}_{12}^1 \text{M}_{21}^2 & \text{M}_{11}^1 \text{M}_{12}^2+\text{M}_{12}^1 \text{M}_{22}^2 \\ \text{M}_{11}^2 \text{M}_{21}^1+\text{M}_{21}^2 \text{M}_{22}^1 & \text{M}_{12}^2 \text{M}_{21}^1+\text{M}_{22}^1 \text{M}_{22}^2 \\ \end{array} \right)$