# Lower bound

• May 9th 2006, 01:21 PM
akscola
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)
• May 9th 2006, 01:42 PM
Jameson
Instead of using the  tags, use the [ math ] ones. :)