## How to show that the matrix $[\min(x_i,x_j)]$ is positive semi-definite?

Well, I want to show that a function is a valid kernel function . The function is,

$$k(x,z)=\min(x,z)$$

Thus, I formed a $$N\times N$$ Kernel (Gram) matrix,

$$K=[k(x_i,x_j)]$$

for a data set $$x_i$$, $$i=[1:N]$$

How do I show that this matrix is Positive Semi-definite Page 4 of the pdf?