Is this Matrix Invertible? Suppose $X$ is a real $n\times n$ matrix. Suppose $m>0$ and let $\operatorname{tr}(X)$ denote the trace of $X$. If $\operatorname {tr}(X^{\top}X)=m$, can i conclude that $X$ is invertible?
Thanks 

The fact that $\operatorname{Tr}(X^TX)$ is positive just mean that the matrix is non-zero. so any non-zero matrix which is not invertible will do the job.
