A method for generating infinite positive self-adjoint test matrices and riesz bases

In this article we propose a method to easily generate infinite multi-index positive definite self-adjoint matrices as well as Riesz bases in suitable subspaces of $L^2({\mathbb{R}}^d)$. The method is then applied to obtain some classes of multi-index Toeplitz matrices which are bounded and strictly positive on $\ell^2({\mathbb{Z}}^d)$. The condition number of some of these matrices is also computed.