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Assume the two sets of vectors $\{\mathbf{a}_1,\ldots,\mathbf{a}_N\}$ and $\{\mathbf{b}_1,\ldots,\mathbf{b}_N\}$ of equal length. My goal is to find the optimum matrix $\mathbf{C}$ to the following ...

Let A be an $m\times n$ matrix and $k$ be an integer. Assume that $A$ is non-negative. We want to find a scalar $\epsilon$ and an $n\times n$ matrix $B$ such that $A\leq A(\epsilon I + B)$ (where $\...