Suppose $M$ is a square matrix (with elements that are continuous functions which are bounded above and below) and $v$ is a vector. I want a lower bound like $|Mv| \geq C|v|$ for constant $C$.
Do I have any luck here?
Suppose $M$ is a square matrix (with elements that are continuous functions which are bounded above and below) and $v$ is a vector. I want a lower bound like $|Mv| \geq C|v|$ for constant $C$.
Do I have any luck here?
There can't be a better lower bound than $0$, because it is possible to have $Mv = 0$ with $v \ne 0$.