Let $k_{nm}=f(x_n,x_m)$ be a function generating the entries for a positive semi-definite matrix $K$ from two vectors $x_n$ and $x_m$. For example, $k_{nm}=x_n^Tx_m$ the inner product (also called the Kernel function and $K$ the Gram Matrix).
Now let $k'_{nm}=k_{nm}+\theta$ a new generating function for matrix $K'$ where $\theta$ a constant (scalar). Is this matrix again positive semi-definite or what are necessary restrictions on $\theta$ to have it psd. (e.g. $\theta>0$ I can imagine)?