6 problems

Let $\widetilde{A}$ be an $n\times n$ matrix satisfying $\|\widetilde{A}\|_2\leq\sqrt{n}$, and let $A$ be a Gaussian perturbation of $\widetilde{A}$ with variance $\sigma^2\leq1$.…

Condition-number monotonicity conjecture. For the Gaussian or inverse multiquadric RBF,

Let $m\geq 4$ be an even integer, let $\boldsymbol{E}_m$ denote the vector set defined in the paper, and let $\beta_{\boldsymbol{A}}$ be the condition number associated with…

Finite expected angular condition number conjecture.

Let $n_1,n_2,n_3$ satisfy $n_1 \ge n_2 \ge n_3 \ge 3$, and let random rank-$1$ tuples of length $r$ in $\mathbb{R}^{n_1 \times n_2 \times n_3}$ have their expected condition number…

For frequency indices $k_1$ and $k_2$, let $\hat L^{k_1,k_2}$ be the corresponding block of $\hat L$, and write $\kappa(\hat L^{k_1,k_2})$ for its condition number. Condition-numbe…