# Invertibility of infinite order matrix

how the matrix $[e^{-(x_j-x_k)^2}]$ is invertible where $\{x_j\}$ be any real sequence such that $(x_{j+1}-x_j) >0$ for all $j \in Z$ where $Z$ denotes the set of integers.

• Is this actually true? I would expect one would need there to exist a constant $\gamma$ that uniformly bounds the differences away from zero, as $(x_{j+1}-x_j) \ge \gamma > 0$. – Nick Alger Dec 30 '15 at 22:52