Past exam of the advanced topics in statistical machine learning course of the University of Oxford / 2025 / 2 / b / ii / Solution

Choose two inputs $0<a<b$. Their proposed kernel matrix isThe coefficient vector $\alpha =(1,-1{)}^T$ givesThus $K$ is not a positive semidefinite matrix, andEquivalently, its determinant $ab-b^2=b(a-b)$ is negative.