All Questions

Suppose a matrix equation $Ax = b$ has no solution ($b$ is not in the column space of $A$) How can I find a vector $x^\prime$ so that $Ax^\prime$ is the closest possible vector to $b$?

My apologies if this isn't a well-enough-posed question, I think I'm partly unsure of what exact question to even ask. There are many different ways in which we can take a function of a matrix. We ...

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 $\...