This paper challenges theoretical aspects by providing a spectral representation that uniquely characterizes space-time positive semidefinite kernels that are axially symmetric on the sphere and stationary in time. We also address the problem of partial Fourier inversion and show that it is feasible ...
II. Positive-definite kernelsDefinition (positive-definite kernels). A kernel k:Rd×Rd→Rk:Rd×Rd→R is positive-definite, if for any finite set of elements xi,…,xnxi,…,xn in RdRd, the kernel matrix is positive-semidefinite (that is, all its eigenvalues are non-negative)....
semidefinite programmingHessian matrixThere exists a large set of real symmetric matrices whose entries are linear functions in several variables such that each matrix in this set is definite at some point, that is, the matrix is definite after substituting some numbers for variables. In particular,...
Elementary symmetric polynomialsMatrix-tree theoremWe prove that the hyperbolicity cones of elementary symmetric polynomials are spectrahedral, i.e., they are slices of the cone of positive semidefinite matrices. The proof uses the matrix-tree theorem, an idea already present in Choe et al....