All Questions

Let $\mathbf{X}$ be $(n \times p)$-dimensional random matrix ($n > p$) whose rows $\mathbf{x}_i$ are i.i.d. with some finite moments: $$ \mathbf{X}^\top = [\mathbf{x}_1, \ldots \mathbf{x}_n]^\...

Let $\mathbf{X}$ be $(n \times p)$-dimensional data matrix ($n > p$) whose rows $\mathbf{x}_i$ are i.i.d. with some finite moments: $$ \mathbf{X}^\top = [\mathbf{x}_1, \ldots \mathbf{x}_n]^\top. ...

Let $\mathbf{V}$ be a $p\times p$ orthogonal matrix (i.e., $\mathbf{V}\mathbf{V}^\top = \mathbf{V}^\top \mathbf{V} = \mathbf{I}$) whose columns are $$ \mathbf{V} = \begin{bmatrix} \mathbf{v}_1 & \...

Considering Schrödinger operators $$ H(\hbar) = \hbar \Delta + V $$ where $V$ is some potential, perturbation theory tells that the eigenvalues of $H(\hbar)$ are holomorphic on some region containing ...