Description: Introduction to linear algebra. Systems of linear equations, matrix algebra, vector spaces, determinants, eigenvalues and eigenvectors, diagonalization of matrices, applications. Not open ...

Refined estimates for finite element or, more generally, Galerkin approximations of the eigenvalues and eigenvectors of selfadjoint eigenvalue problems are presented. More specifically, refined ...

We show that in a common high-dimensional covariance model, the choice of loss function has a profound effect on optimal estimation. In an asymptotic framework based on the spiked covariance model and ...