Let X0 be a square matrix (complex or otherwise) and u0 a (normalized) eigenvector associated with an eigenvalue λ 0 of X0, so that the triple (X0,u0,λ 0) satisfies the equations Xu = λu, u0 * u=1. We ...

In applying statistical methods such as principal component analysis, canonical correlation analysis, and sufficient dimension reduction, we need to determine how many eigenvectors of a random matrix ...

In chemistry, the properties of atoms and molecules can be determined by solving the Schrödinger equation. However, because the dimension of the problem grows exponentially with the size of the ...