# Math Help - Lower bound

1. ## Lower bound

Hi

Given a set of $n$ matrix $A_{1..n}$, size $p \times q$ such that $\forall a_{ij}\epsilon A_{z},z=1..n : 0\leq a_{ij}\leq1$ , $\sum a_{ij}=1$ and $H_{z}= \sum_{i,j}a_{ij} \log_{2}a_{ij}, a_{ij}\epsilon A_{z}$.
Find a bound (minimum) for $\sum_{i,j} \frac{\prod_{1}^{n} A_{i}}{\sum_{i,j} \prod_{1}^{n} A_{i}}log_{2} \frac{\prod_{1}^{n} A_{i}}{\sum_{i,j} \prod_{1}^{n} A_{i}}$ as a function of $H_{z},z=1..n$
PS: AB is the element-by-element product of the arrays A and B(such as A.*B in matlab)

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